diff --git a/src/SVM.ipynb b/src/SVM.ipynb
index b82657e..293b8a6 100644
--- a/src/SVM.ipynb
+++ b/src/SVM.ipynb
@@ -1,1482 +1,1482 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Support Vector Machines"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"New R commands:\n",
"- `svm(formula, data = , kernel = , cost = , scale = )` fit an SVM\n",
"- `tune(svm, formula, data = ,kernel = , ranges = list(param = )` tune an SVM with cross-validation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the `e1071` library in R to demonstrate the support vector classifier\n",
"and the SVM.\n",
"\n",
"The `e1071` library contains implementations for a number of statistical\n",
"learning methods. In particular, the svm() function can be used to fit a\n",
"support vector classifier when the argument kernel=\"linear\" is used. This\n",
"function uses a slightly different formulation from the slides (or equations (9.14) and (9.25) in the book) for the\n",
"support vector classifier. A cost argument allows us to specify the cost of\n",
"a violation to the margin. When the cost argument is small, then the margins will be wide and many support vectors will be on the margin or will\n",
"violate the margin. When the cost argument is large, then the margins will\n",
"be narrow and there will be few support vectors on the margin or violating\n",
"the margin.\n",
"We now use the svm() function to fit the support vector classifier for a\n",
"given value of the cost parameter. Here we demonstrate the use of this\n",
"function on a two-dimensional example so that we can plot the resulting\n",
"decision boundary. We begin by generating the observations, which belong\n",
"to two classes, and checking whether the classes are linearly separable."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Support Vector Classifiers"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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WrP3z/y7ofv9an3wE2DZq3FWQAArK41v2K3//UT9v/xrw+8YdiBa2UOAABrypsn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\nIewAAEJC2AEAhISwAwAIiT8AKPOTmKZTVJYAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"set.seed(1)\n",
"x=matrix(rnorm(20*2), ncol=2)\n",
"y=c(rep(-1,10), rep(1,10))\n",
"x[y==1,]=x[y==1,] + 1\n",
"plot(x, col=(3-y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"They are not. Next, we fit the support vector classifier. Note that in order\n",
"for the svm() function to perform classification (as opposed to SVM-based\n",
"regression), we must encode the response as a factor variable. We now\n",
"create a data frame with the response coded as a factor."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"dat=data.frame(x=x, y=as.factor(y))\n",
"library(e1071)\n",
- "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=10,scale=FALSE)"
+ "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=10, scale=FALSE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The argument scale=FALSE tells the svm() function not to scale each feature\n",
"to have mean zero or standard deviation one; depending on the application,\n",
"one might prefer to use scale=TRUE.\n",
"\n",
"We can now plot the support vector classifier obtained:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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PixbxOLfkr2Xy+NnrLD2vbpVTvW/fjll3Ojt6+d1FG7pt757O9ZlTs8KgBtBwCA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\nSwAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(svmfit, dat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the two arguments to the plot.svm() function are the output\n",
"of the call to svm() , as well as the data used in the call to svm() . The\n",
"region of feature space that will be assigned to the −1 class is shown in\n",
"light yellow, and the region that will be assigned to the +1 class is shown in\n",
"purple. The decision boundary between the two classes is linear (because we\n",
"used the argument kernel=\"linear\" ), though due to the way in which the\n",
"plotting function is implemented in this library the decision boundary looks\n",
"somewhat jagged in the plot. (Note that here the second feature is plotted on the\n",
"x-axis and the first feature is plotted on the y-axis, in contrast to the behavior of\n",
"the usual plot() function in R.) The support vectors are plotted as crosses\n",
"and the remaining observations are plotted as circles; we see here that there\n",
"are seven support vectors. We can determine their identities as follows:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
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"1. 1\n",
"2. 2\n",
"3. 5\n",
"4. 7\n",
"5. 14\n",
"6. 16\n",
"7. 17\n",
"\n",
"\n"
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"[1] 1 2 5 7 14 16 17"
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},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"svmfit$index"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can obtain some basic information about the support vector classifier\n",
"fit using the summary() command:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 10, scale = FALSE)\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: linear \n",
" cost: 10 \n",
"\n",
"Number of Support Vectors: 7\n",
"\n",
" ( 4 3 )\n",
"\n",
"\n",
"Number of Classes: 2 \n",
"\n",
"Levels: \n",
" -1 1\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(svmfit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This tells us, for instance, that a linear kernel was used with cost=10, and\n",
"that there were seven support vectors, four in one class and three in the\n",
"other.\n",
"\n",
"What if we instead used a smaller value of the cost parameter?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
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"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 4\n",
"5. 5\n",
"6. 7\n",
"7. 9\n",
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"10. 13\n",
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"16. 20\n",
"\n",
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3t6q1atmpe4m3IDAzBJhB20xu7RJwbk\nnW1N+2vCQ49MWrR6+8FjJ08cObDj9y+mDuwyfkNq7qN1Bw9qV3RXXdfhQ3LLLi4qKklExKLr\niKG1pCz5B+hOb9p0XkSkTadO5Tim5NVvUP6P7nPzn3n+x/8uJyXfCNs668VP8yKq1sBBHYvf\nNT09Pe9XGVevxuX96uLPr7y/s8hmFvrwzStWrFixYsXyd6Z88m98bklZudau655/ztXV1dXY\nzSqAcS/ZyFdXVFnXMrgMHjcs76/H1eWjek397VBkbML1sL3fvPToKxvyLqepGzz+sXs871qc\nC0ueHDhn/cnrSSmxZzbNGTphVULuukOvwY+VfOL+7gc2/rIOAFqi9GW5QMW7+POwWmX8P4t1\n4xc2x9+5p37fK4WPz1kGLi3mJmVFb3diMBgMmauGFfrJXG/SodztjL2PXeruVxuXOK97/5+u\n5m52570w9LtfvnXK16ZWuz4D+/Xw9y7yE779hxEGg0F/6sO2Bcu2bvXva9Wqeb0at5ZsO30S\nZvxmFXC7E6NesrGvzmAwxNz6IxEbz6ZtH3z8k6Mlz3n5h4ElnvkUsagbvOnmrW0LbnfSY0lM\n4b9iH3XI/6bk/R0oQcHtTiysrIr7ADGb1jOO3LrTXPE3KC7PwCV9KwCYC47YQYNqD/1uz7p3\ngnxLOGxm49tr+oadC4OK+YgFXYfhQ+vf+p1V9xGDPe/c6E7WnTsXHPyr1rlzOU+L2Xf5YMNX\no5rcedTGxrf3gs3fDfMqaUddl7cWPd0w92VmXjr45+rf/z52zTng7Z+ndcvbIjoiIlNE13TS\nml9euj/vBWfERoYePXoyKi73xKDzAy/8tOrlhmL0ZhXBmJds7KsTEfdHBnTJ+1qZ108f2nsg\nPLHk5/YZ8f2OZSMaVbvzEZ2z/5gft3/+yN1fnFEKpydmzupw2+UP1ZqP/2ndlFZlfCRwuQYu\n17cCgPZwuxNoklXd3jM3h796fMua9TsPHg+7FJuUZrBxdPVu0KJ94OODHmvlXuKP0g6jXh1w\n8Lc4ERFd6+cGFfMZTWJVs1VAQLaIiE2zvCMpPt2HDQrQ3RARkRb9OuX+d2Xl4x8QkJ67XXFf\npxBrv6e+Pf7w879+v3rbobPRcWmW1T3rtwrsN3J4zwYFP86d/DoGBNQTEWnim19EXn2/On5m\n2LIlq/eduhhv6dGofa+ngoe08QxdtGqHPkZE5PQva670GOajq93v0wPhYzeuWv3XvuOR1+JT\nsq2quXrVb96+54Chvfzd84+0GblZ9YYPBgTEiIjUL/QRCuLeLCAgIEdEpIVnwcEp+7ptAwJc\nRER86zuW7yUb++pE6r+w4d/ay778fd+p6LiUzBzX3I+9L2FOsWv+7A+hfV9b+/Oav/afir6R\nmG3j7Fm3xYNBA4f18a9R5P92XRp3DghIEBFpVbPw3xnbOg8EBNjl/tmWcjStCPu2b+8Kfeir\nz77dfvxivLj6tX14xOhRXWoV/rLF/RGXb+CSvhUAzIXOYOxNmAAA5ZT+XR/7UetFRJzHbY1f\n2lPpeQBoHadiAQAANIKwAwAA0AjCDgAAQCO4eAIAKo2FV8uAgGQREcfGFXIPQAAoFRdPAAAA\naASnYgEAADSCsAMAANAIwg4AAEAjCDsAAACNIOwAAAA0grADAADQCMIOAABAIwg7AAAAjSDs\nAAAANIKwAwAA0AjCDgAAQCMIOwAAAI0g7AAAADSCsAMAANAIwg4AAEAjCDsAAACNIOwAAAA0\ngrADAADQCMIOAABAIwg7AAAAjSDsAAAANIKwAwAA0AjCDgAAQCMIOwAAAI0g7AAAADSCsAMA\nANAIwg4AAEAjCDsAAACNsFJ6gBKkxZwLi4pJtaxRr2ljbwed0uMAAACon/qO2GVf/OOtRxt4\nejVq1b7Tg22a+tTwDXxldWR2KXtk/jzU1uoOdiPXVdnMAAAAKqC2I3YpOyf17L/grK3fIy9M\nCvKzvXF03YqVOxcM6Zn199HFgY7F7xN5Liwzx/W+gOYehVctm9SoioEBAADUQmcwGJSeoZAb\nX/TwGbut9rN/HVnWw1lERPSXvuzbYvT6xAc/PvfPxPrF7rRpjMtja4Zti/28W1WOCgAAoDLq\nOhWbunnDzmxpPea1vKoTEYtawS8NdhL9vq3bkorfKS4iIkEaNmxYVUMCAACok7pOxV66cCFH\nbFq0aFxk1dXVRSQpKSlFxKmYnSIiIsS2k1+tyhzs6NGj2dmlvc8PAIB7YWVl1apVK6WnKBAW\nFpaYmKj0FAXU9v1RLXWFXYOX/4p51mDvXPgqWP3JTVsvirg2aeJZ7D5ZERHRUs8l7svJw37Y\nEXo13c6n2UMDn584NrC2dQVNdejQoXbt2lXQFwMAoHgHDx5s27at0lOIiGRnZzdr1iwnJ0fp\nQYpQz/dHzdQVdpYOru4OhRf0Vza+MuL9I2LRaPz4h4s/bXw+IiJHzix59ll77/ta+tqkhIWs\nOrRt1dc/ztyw+Z2O1cp6RoPBsHv37szMzFK2OXnypIhkZOy2samoVkTZpupGKT0CAFSiVpI0\nSK5uE7cdUiNHDHPkXOk/jKqSXq/PycnpLZ4PiHPZW1e+TNF/IOHq+f6ombrCrojkU99PGf3y\nwr2x4vnIgl+ntyth1MjISNHVenz+um9ffMDFQiTr4pZpQwe/v+fdIW90CVsUaFf6k0RGRgYF\nBWVkZJQ5TlZWNmFXlWYYVtJ2ADTsmtiISF1JU3oQaIq6Lp7IlxHxx7uP3Nf6yU/3JtYOmr75\n8PqX/G1K2jZw3vmbCefWTHjAJfe1WNcJmvPzjC4WEv3tV1vLPIjcoEGD9PR0Q6mWLl0qIuq6\nfNg8zDCsVHoEAKgsV8X2utj4SWoDSVV6FmiH+sIu5+Lq5zu06jtry1WPHpN+OHpy87SHa1mW\nsr21g4uLk13RLXwDutYTSYqKiqvUUVH5aDsAGrZWvDLF4im5PEyuKj0LNEJtYZf414QeQ5cc\n1bd4+uvDp/76aESz4q6DLSQ16uCOHTtDb9y2nJ6eLmLh7FzG3jAFtB0ArYoWu2VS57RU44Qs\nKorKwu7k/JeXhInf2LW7vvq/FsZUWcamt7p3Cxy8+GThxZyDv6+/LLq2D3Up4x12MBG0HQCt\nui42P4nPh1L8HfiB8lJX2B3/5edQQ/Xhcz952LWkTZIO/7Jo0aIVuy7l/ta13/Agezn18Zg3\ntlzMvQAiI+qPic8uOCNug14PblAlU6Mq0HYAAJRJVWGXsn9/qEjyqpFejnca8E2KiEjslg9f\neumlN34Jy9vHJ/jzFU81yd734SP13HwaNmno7ebX99OjFv6v/rhkkJuCrwUAAKCqqep2J7FW\nPgEBASU82MjdQkTEzrdNQICjcyOX/HWLuiO+OR44duXSH3cdD7+SbtfusQd6DAse2aVWidfR\nwkRxAxQAAEqnqrDzffqrHU+XsY33E5/veOL2RWufzsHvdQ6unKmgIrQdAAClUNWpWKBsvNkO\nAICSEHYwPbQdAADFIuxgkmg7AADuRNjBVNF2AADchrCDCaPtAAAojLADAADQCMIOpo2DdgAA\n3ELYweTRdgAA5CLsoAW0HQAAQthBM2g7AAAIO2gHbQcAMHOEHTSFtgMAmDPCDlpD2wEAzBZh\nBw2i7QAA5omwAwAA0AjCDtrEQTsAgBki7KBZtB0AwNwQdtAy2g4AYFYIO2gcbQcAMB+EHbSP\ntgMAmAnCDmaBtgMAmAPCDuaCtgMAaB5hBwAAoBGEHcwIB+0AANpG2MG80HYAAA0j7GB2aDsA\ngFYRdjBHtB0AQJMIO5gp2g4AoD2EHQAAgEYQdgAAABpB2AEAAGgEYQcAAKARhB0AAIBGEHYA\nAAAaQdgBAABoBGEHAACgEYQdAACARhB2AAAAGkHYAQAAaARhBwAAoBGEHQAAgEYQdjBfMwwr\nlR4BAICKRNjBrNF2AAAtIexg7mg7AIBmEHYAbQcA0AjCDhCh7QAAmkDYAXloOwCAqSPsAAAA\nNIKwAwpU2UE7C0kYItHBcqNhwZrBW64ES/RgyeQ/SwDA3eEnCFBE1bSdXpyOS1Y9udlXUq1F\nREQn8f0kuZ5YHRcbfRVMAADQIsIOuF2VtJ3FafE4IeIiMd3EIJLVQWJrieUx8ThT+c8NANAq\nwg4oRpW0neN6cUyVzE4S10iu9xBDsnhuEMvKf14AgGYRdkDxqqDtUsRzg1haSNyTkmorjn+K\nY2plPyUAQNMIO6BEld92lsfE9bKITuS8eIRW8pMBADSPsANKU8ltZ6gtiT4iIlJHEnwq85kA\nAOaAsAMUYylxAyRTpPpusbSQmwMkg/8gAQD3gp8jQBkq7aBdRqDc9BCrQ+KxVTzOiMFbrj0k\nhsp5LgCAWSDsgLJVQtvlZVyKePwlFiJOf4pDpmQEyE2Pin4mAID5IOwAo1Rs2+WfeK22SRzT\nREQkQTy3ic5K4vpLpq4CnwkAYE6slB4AMBkzDCun6kZVyJeyFodNYm8Qm6hCa/ukzmXR60Rn\nLZJZIU8DADAzHLEDyqGijttliF2k2EcVvR2xXmyjxD5SrKk6AMDdIeyA8qmaD5MFAOAuEHZA\nudF2AAB1IuyAu0HbAQBUiLADAADQCMIOuEsctAMAqA1hB9w92g4AoCoqDLvsC5v+90zPFrVr\nONjaVfdp+tDI6WvD00vfRX9tz+JxPVvUcXWoVqNO614vLNkbWzWzArQdAEA91BZ2hvNfD3yg\n11tf77zq0qrno4EtHK7u+eG9AR0HLo8q+SM0b26bGNj9xWW7b9bsOqB/YN34HZ89H9hxwl8J\nVTg2zBptBwBQCZWFXfqfb7/yR2y1Lu8fjDqxfd3vm/45e3rT+GaWNza+OvmX+OJ3yfl39tgF\npw2t3t51ev/v33+/OuTUvlnt5NzC0e/+k121w8OM0XYAADVQV9hlb/319wTxffaDN1o75q5Y\negd9PG2AjST/sWpTRnG7ZG1atCxc3J6cM62DU+6Kvf+kyf3t5cI3y7dQdqg6tB0AQHHqCrvL\nYWEpYtHxwfaFPwTdoWHDmiIZly8X+765wzt2JIntw7172hSs2QYEdBRJ3Lnzv0qeFyiCtgMA\nKEtdYef8yPRVq9a8GWBVeDHu6NFoEduaNd2K2SPhyJEokYbNm9sUXvVs3txdJCosLKsypwXu\nRNsBABRkVfYmVci5edDg5kVWsi/8PO7djdlSfeCwR22L2SM2NlZEvLy8ii67urqK3IiLSxBx\nL+tJT5w4kZFR7GnePBcuXCh7dAAAAKWpK+yKSj+3Znrw+I92X7eoM3zZvCEuxW2TmJgoIra2\nt0VftWrVRCQ7u8w32YWHh/v7+xsMJV9zm8+YbQARmWFYOVU3SukpAADmSF2nYm/JuvT3nIEt\nWw78YHesZ/d3Nuz/bljN4je0trYWkbS0tKLLmZmZIuLg4FDWE/n5+SUmJsaV6pNPPhERnU5X\n1hcD8nBCFgCgCBUescs69/OEIWOXHkm0cG8/duFn/xvdxrXkpPL09BQ5HR8fL1L4LXgxMTEi\n1WrWrG7E8zk6Opa+gRF9CNyO43YAgKqntiN2+oivBncesfSIvsXTS/ef3ff5mNKqTkQ8mjZ1\nEzl9/HiRyyTiw8JiRPz9/St3WKBUHLcDAFQxlYXdtW+ee3HddYcHZ+/c99W4tqU3Xa7OPbrb\nSfq2zbsKlV3ixg0hIk2Cgnwrb1LAGLQdcllIwhCJDpYbDQvWDN5yJViiB0umyv4hBmDC1PXv\nyeVV32xNtXxozk9vP1CthE2yboSfOHHi9JWUvN879Bs/ykeufP3G7EO5S/qrf772ztpkh24T\nxrSokqGBUtF2EBG9OB2XrHpys6+kWouIiE7i+0lyPbE6LjZ6hacDoB2qeo9d1o5tIQZxuL7m\n+T5b7niwzYRf3wuyk0vLh7V861+3F7bfWBQoIiK23d9fNnpz/xXvdW68vmfHOmmh23eejncJ\nXLR4XO0qHh8oAe+3g4jFafE4IVdaSEw38d0i2R0ktpZYHhOPM0pPBkBLVBV25yMickSSzuxY\nX8y/dNn9S7p3iVufZfu2NH3rvS827lofaut9X/8335j97uCmlpU6KwCUk+N6cWwgyZ0kLlLS\ne4ghWTw3CP9SAahIqgq7hu8cMbxTxjb13jxkePP2RQuf7pO+7j6pksYC7h0H7fF+5Z8AACAA\nSURBVCAiKeK5QdIGS9yTIjpxXCOOqUqPBEBj1PUeO0DDeLMdRCyPietlEZ3IefEIVXoaANpD\n2AFVh7Yze4bakugjIiJ1JMFH4WEAaBBhB1Qp2s6cWUrcAMkUqb5bLC3k5gDJ4J9gABWLf1WA\nqkbbmauMQLnpIVaHxGOreJwRg7dce0j4EGoAFYmwAxRA25mfvIxLEY+/xELE6U9xyJSMALnp\nofRkALSEsAOUQduZlfwTr9U2iWOaiIgkiOc20VlJXH/JNOJDdgDAKKq63QlgXrgHivmwFodN\nYm8Qm6hCa/ukzmXR60RnLZKp2GgANIWwA4BKlyF2kXcs6sU2qqoHAaBxnIoFAADQCMIOAABA\nIwg7AAAAjSDsAAAANIKwAwAA0AjCDgAAQCMIOwAAAI3gPnYAAJRGJ9nukm0nFvFik6T0MEDp\nCDsAAEqS2UquB0maU95vraLEfZ043VB0JqAUnIoFAKBY2W0kepCkZ4nrJvH+Tdz3iq6OXH1W\n4t2UngwoCUfsAAAohq3ceFRyUsV7mTiliojIUal+Uc4PldiHpfpPHBmBKvH3EgCAOxkaS7Kt\nWB/OrzoREbE8KU5Jom8sqZbKTQaUgrADlDTDsFLpEQAUK9NbDCK20UVXDWITI2IlWY7KTAWU\ngbADFEbbAaqktxERsUwt4WFdFY4CGI+wA5RH2wHqY5kmIpLtdPt6lqtIjlglV/1EgBEIOwAA\n7mQTLRYiac1EX3jVR1JcRS6KfbZScwGlIuwAVeCgHaA258QlVvT3yfUWYshdcZC4XpIp4rSH\ne0pArfirCajFDMPKqbpRSk8BII9eavws6f8nSUMl5TGxTpPsGpJjJbYh4nFG6dmAknDEDlAR\njtsBaqK7KrUWivffUu2yWCaIw2HxWiF1tgi3OoF6ccQOUBeO2wGqkipOO+WOKygAteKIHaA6\nHLcDANwdwg5QI9oOAHAXCDtApWg7AEB5EXYAAAAaQdgB6sVBOwBAuRB2gKrRdgAA4xF2gNrR\ndgAAIxF2gAmg7QAAxiDsANNA2wEAykTYASaDtgMAlI6wA0wJbQcAKAVhB5gY2g4AUBLCDgAA\nQCMIO8D0cNAOAFAswg4wSbQdAOBOhB1gqmg7AMBtCDvAhNF2AIDCCDvAtNF2AIBbCDvA5NF2\nAIBchB2gBbQdAEAIOwAAAM0g7ACN4KAdAICwA7SDtgMAM0fYAZpC2wGAOSPsAK2h7QDAbBF2\n5bBz53+Bgc+NG/c/pQcBykDbQRP0vhLXTeLaiL7QYmYLie0mCb6KTQWoGmFnrIyM7LFj39+9\n++hTT/VSehagbLQdTJ9FjGS1k9h+cqNB/pKHXBskcW3F6rqSgwHqRdgZ66OPvjt79sJLLw3p\n3Nlf6VkAo9B2MHVp4v6nWIokPC5pViI6ie8n6Zbi9IdUS1d6NkCdCDtjzZv3Y4MGtebMeU7p\nQYByoO1g4ixDxfOkiJtcf0iy2kqsr1geE4/TSo8FqJaV0gOYjKys7BUrpjg42Ck9CACYFcc/\nxbG+JD8kF7NFnyI+G8RS6ZEA9eKInbF69+4cGPiA0lMA5cZBO5i6FPHcJBZWkmMn1daLY6rS\n8wBqxhE7Y23bdig8/JKfXy2lBwEAc5PllXdhbJanGER0Co8DzYg58sfOcxlGbuxxf98AP5tK\nnaciEHbGSk1Nf/bZOX//vUin498UAKgyhtpy7UGRG2JvL2kPSVyouF1VeiYoYvXq1SdOnChl\nAysrq5EjR9ra2hr7FU8uf2bI4lgjNw5YGLPjRXdjv7RiCDtjdezYfPv2f5ctWztu3AClZwEA\nc2Epcf0l00Kc14lbdTk/WG4OEMfPxVZf9q7QDr0YROTXX391dy+trKysrIKCgmrXrm3s1+00\nfefm1svnvLtg51WD1O75/LBW9iVv7He/g/ETK4ewM9ann77WufPY119f1Lt359q1PZUeBwDM\nQUaA3PQUyyPiHiUWIu6t5VpDudZZfHcrPRmqkkFERN56661x48ZV5Ne1cW8eNGZeYOMMv4Al\n0X6D3ps7Xv1H5MrCxRPGatas3uTJTyYmpvDJEwBQNbzk2kNiSBOPzXk/rar/IfZZktFNbpr+\nz1+ohk3XQX08lB6iwnDErhxmzx4/e/Z4pacAADOR6SbVdonTRXFKyV+6KV6/SqK3iLvIDSVn\ng6a07PJY890WNTTRRJp4EQAADbIJFbfQ2xetT4nbKSWmgYZ5jvzmxEilh6ggnIoFAADQCBUf\nscvZEuz+yIaR268uCix9Q/2u2Y/N2J5z26pltxmbp3SqrOEAAABUR71hF/Pz56vjxZgP8Io+\ntH7L33tvX7V0f7ESpgIAAFAt1YVd2rWT/x0+sm/rT58t/TNBjAq7iIgIcXhqQ8o3j1X6dAAA\nAOqlurDbP7NHt8XXyrNHakTENfHz86usiQAAAEyD6i6eaD5m+apcbwZaG7VHRESEWDZsWL+S\nBwNM1wzDSqVHAABUBdUdsfNo3WdwaxERsfvzSWN2MERGnpc6j3ueW79k1Y7Qq+l2Ps0eGjCi\nTwtX1TUroKAZhpVTdaOUngIAULlUF3bldjkiIl1ivhjsPzchO29p7rR3Okz+6fcPgryM+QJX\nrlxJS0srZYMbN7gLJgAAMAGmH3YREREiWe49P/h55qiu9axjQrd8/vrL72/7cMCg2sdCXirr\nnXfh4eENGzY05nkMBkMFTAsoh4N2AKB5ph92DUctW/Nw7Q692vhYiIj4thk6+0/vZP+AT/d8\nsDDkpfldSt/bz8/vwoULWVlZpWzz448/vvPOOzqdrgKnBhRB2wGAtpl+2Pm07df/tiX7rkN6\ne3264NKxY3HSpUZZX6BOnTqlb+DuzodNQztoOwDQMI1eYeDk5CQiVlam361AxeMiWQDQKlMP\nu+i5HXU6XdfPit757lJISKRIg/vvr67QWIDK0XYAoEkmF3ZZN8JPnDhx+kpK7m9rBz1yn0jI\nJ1P+vK7P2yIn+pdX5+zIsbp/bHA7xcYEVI+2AwDtMbmwu7R8WMuWLbvMPpj3e//XFr98n234\nir5N7us5Ysy4McN7Nms+fNXl6l1mf/lqE0UnBVSPtgMAjTG5sLtD9cD5B46tmfWkv9W5zd9/\n/cPm07ZtR81cc3Dz661tlB4NAACgKqn46oI+X6cbvr5jtd6bhwxv3rZWrVH/Kd/2n1IlUwHa\nwkWyAKAlpn/EDsC94YQsAGgGYQeAtgMAjSDsAIjQdgCgCYQdgDy0HQCYOsIOQAHaroLoG8ml\nYIkeLJmFPmQ65TGJDpYbjZQbC4DmEXYAiqDtKoJFuDhYS5q/XM+/T7q+iVx/UNKtpHq4opMB\n0DbCDsDtaLt7pxfXtWKbI2k9JdFRxEZu9JHsHKmxVmz0Ze8NAHeJsAOASnFNvHaLzk5u9JKU\nHpLgLLY7xPW60lMB0DbCDkAxOGhXEWx3iut1yWkhlzuK7op47RZd2TsBwD0g7AAUj7a7dzlS\nY4tYiohOqm8WW07CAqhshB2AEtF29yy5veQU/QUAVCLCDkBpaLt7kNNKYhqLRZi4XJWc++R6\nc6UHAqB5hB2AMtB2d6eaXO8lOVni9qe4/y42BknuLcn2Sk8FQNsIOwBlo+3KL7mPJNuL7U5x\nuSm6S+K5X8RRrvfihCyAykTYATAKbVceeSdeb4jnnrwV+7/FOTHv5CwAVBYrpQcAAA2KFZ+v\nRBcndrcO0GWI+5fi5CySouRcADSOI3YAjMVBO6NZXhP7SLFLKLJoESf2kWLPPYoBVB7CDkA5\n0HYAoGaEHYDyoe0AQLUIOwDlRtsBgDoRdgDuBm0HACpE2AG4S7QdAKgNYQfg7tF2AKAqhB2A\ne0LbAYB6EHYAAAAaQdgBuFcctAMAlSDsAFQA2g4A1ICwA1AxaDsAUBxhB6DC0HYAoCzCDkBF\nou0AQEGEHYAKRtsBgFIIOwAVj7YDAEUQdgAqBW0HAFWPsAMAANAIwg5AZeGgHQBUMcIOQCWi\n7QCgKhF2ACoXbQcAVYawA1DpaDsAqBqEHYCqQNsBQBUg7AAAADSCsAMAANAIwg4AAEAjCDsA\nAACNIOwAAAA0grADAADQCMIOAABAIwg7AAAAjSDsAAAANIKwAwAA0AjCDgAAQCMIOwAAAI0g\n7AAAADSCsANQRWYYVio9AgBoHGEHoOrQdgBQqQg7AFWKtgOAykPYAahqtB0AVBLCDoACaDsA\nqAyEHQAAgEYQdgCUwUE7AKhwhB0AxdB2AFCxCDsASqLtAKACEXYAFEbbAUBFIewAKI+2A4AK\nQdgBUAXaDgDuHWEHQC1oOwC4R4QdABWh7QDgXhB2AAAAGqHisMvZEuyq835xhxGb6q/tWTyu\nZ4s6rg7VatRp3euFJXtjK3s6AJWEg3YAcNfUG3YxP3++Ot6oLW9umxjY/cVlu2/W7Dqgf2Dd\n+B2fPR/YccJfCZU8IIDKQtsBwN1RXdilXTv5z8bvP5n4+INjVhuVZjn/zh674LSh1du7Tu//\n/fvvV4ec2jernZxbOPrdf7Ire1gAlYW2A4C7oLqw2z+zR+deT74278/wNKO2z9q0aFm4uD05\nZ1oHp9wVe/9Jk/vby4Vvlm+h7AATRtsBQHmpLuyaj1m+KtebgdZGbH94x44ksX24d0+bgjXb\ngICOIok7d/5XaWMCqAoV2Hb2klZf0upKTuHFapJWX9J8xFBRzwIAylJd2Hm07jM4V+e6RgyX\ncORIlEjD5s1tCq96Nm/uLhIVFpZVSVMCqCoV1XbZktJXokfLNf+CtYQhEv2MxHmLrkKeAgAU\np7qwK6fY2FgR8fLyKrrs6uoqoo+L4wIKQAMqpO2yxG2tWBsk5VFJthMRyWktNxqIxTnx4tg+\nAM2wUnqAe5SYmCgitra2RZerVasmItnZZb7JLjw8vGnTpkZsKAYDJ2sAk6Y7L14HJLqDxDws\nDn9LzKOizxDP303+n0EAKGDq/6JZW1uLSFpamohDoeXMzEwRcXBwKGG3W/z8/A4dOlR62K1e\nvXrOnDk6HSdrAMXMMKycqht1z1/Gfqs4N5GEtnLZU9IcxP4Pcea4PgAtMfWw8/T0FDkdHx8v\n4lZoOSYmRqRazZrVjfgSrVq1Kn2DQ4cO3cuIACrE3bZdhr8ku4nlBXEJF8kU93WS8pSk1RXd\nTal+uuLHBAAlmfp77DyaNnUTOX38eJHLJOLDwmJE/P39S9oNgCm6qzfb2cRLcqDEDJWkaiIi\nFgliqRcRMViIXVLFzgcASjP1sJPOPbrbSfq2zbsKlV3ixg0hIk2CgnyVmwtApSh/2+kuiOd+\nEXuJeUT0OokfJBkWIgYRZ4mvXykzAoBiTC7ssm6Enzhx4vSVlLzfO/QbP8pHrnz9xuxDuUv6\nq3++9s7aZIduE8a0UG5MAJWm/G1n/5e4xEtOa7neW27UFBGx3ytWIgn9Jc2Y+2UCgKkwubC7\ntHxYy5Ytu8w+mL9g2/39ZaN9s/59r3Pjdr0HDezevFm/5REugR8uHldbyTkBVKLytl2muP0u\n1iJJ7cWQe3nsJvE8KuIq13pyd2IAGmJyYVcMtz7L9m356P86Ol7YtX7zsbSG/d9ctWf9C80s\nlZ4LQCUqZ9tZREi1ZBER0Yv7b2ItUm2jOKZKVke5UadSBgQABaj4qtg+X6cbvr5jtd6bhwxv\n3r5o4dN90tfdJ1XFVABUozzXyRrqSmruWVcLyawhEi+SKp5/ir69ZLaS7Itq/scQAIzGv2UA\nzEF2LcmyFavzovOVhH7iuFgcMsXyhNQ6ofRkAFCBtHAqFoDZMvKEbA251l0MqeLxo3geFnGV\n6z1FX9mzAUDVI+wAmLYy206Xd/Wrw2ZxTBWHLeKULFkdJJb7IQHQHsIOgMkrte2y28mNeqI7\nL55HREQkTTw2iqVO4vtLOm9GAaAxhB0ALSi57TKtxGW7eP8u1vn3NbE8Lt4bpcZxyXKvqvEA\noGoQdgA0ooS2c/hH3LaL442ii3vFbbs4Xa2SwQCgyhB2ALTjrj5MFgC0g7ADoCm0HQBzRtgB\nAABoBGEHQGs4aAfAbBF2ADSItgNgngg7ANpE2wEwQ4QdAM2i7QCYG8IOgJbRdgDMCmEHQONo\nOwDmg7ADoH20HQAzQdgBMAu0HQBzQNgBAABoBGEHwFxw0A6A5hF2AAAAGkHYAQAAaARhBwAA\noBGEHQAAgEYQdgAAABpB2AEAAGgEYQcAAKARhB0AAIBGEHYAAAAaQdgBAABohJXSA6DSGZIu\n79504N/whKxq7i0COgX5u/KnDgCAJvEjXtsMVzYsHvh/P+y7oc9fsWs05IVfvhzS2lHJsQAA\nQGXgVKyWZR37pveA7/Zbt53+65dh0X9E/Dd//iifi6s+Dhq1+arSswGKmGFYqfQIAFCJCDsN\nS/5l2jf/ZbqO/uqjaYPua1jLo37rji9/M29OZ8uYtUsX/Kv0dIBCaDsAGkbYaVfWv39sSpN6\nj44Nsi1Y1HmPfKK1yJVt2y4rNxkAAKgUhJ12XYo+ly7SrMF9uiLLnr7ediJXr8YqNBagPA7a\nAdAqwk67MrMyRXS2NjZFl7OSUzNEbG1tit8LMA+0HQBNIuy0y9ujpk4M4dGRRZdDT0YaRNeo\nUS1lpgJUg7YDoD2EnXZVb9OjnYUc3/j1YX3BYnbotz9GiVXrxx/lficAbQdAawg7DfMe8+5j\nPhI9d/jUhVsjr8QlXjn97+L/m74wXNfguWf/z0fp6QB1oO0AaAk3KNYy1z6TNyxM6T/prwlB\nf03IW7NvNnLK2rkP2Cs6GKAqMwwrp+pGKT0FAFSAYsLuyoY5szcYey+Mmr2mvN2Lgz+qZdf6\nxf+dGXhq06Zjp69mWLt6tezaoVtzF3IeuA1tB0AbivkRn3J205ef7U4zGLV/c/fxhJ3K2dZs\n1i+4WT+lxwAAAJWtmLBr+Mqu2IHbPh0/6s2Nl8V3xJLFT9Quef/qjetW3nAAUGU4aAdAA4o/\nKWfv2/2Nb2f+XXP0VqfGgX36NK3ioQBACbQdAFNX8lWx7j17tq7CQQBABbhIFoBJK+V2J3V6\njp/wwhPtXatuGABQHm0HwHSVcn2k7oHgBQ9U3SQAoBackwVgorhBMQAUg+N2AEwRYQcAxaPt\nAJicu79V7fWTO0JjpFq9du3qVavAgQBAPTgnC3N2XBKvSIbSU4iI5Cg9gAm5+7DbNq3biN+k\n+bTjJ6a3qMCBAACAGmT5VEtzcVJ6ChGRnJwcOZug9BSm4e7DroZfmzZtpGFNPnQUgJZx0A5m\na9q0Z8eN66/0FCIicXGJbm5BSk9hGu4+7II+OMT3GIA5oO0AmIp7vHjCkJ6eWTGDAICKcSEF\nAJNQRtidnD9q7JdHEot9LC1s1aTA3h+drYSpAEB1aDsA6ldG2Bni//tidLsWj0zdeKHwkbmc\nqzvnDvRvNfTjXde4UgWA2aDtAKhcGWHX+OkPpgT5XN0ys1eLNk8vPXjTIJJ04pvnO93XbfKa\nc9J44PsLxzatmkEB05Ae9v3M5dOn/7j1UsGaIeqfudOXT5+//7Jyc6Gi0HYA1KyMsLOp13vW\n5tD/vn+ls/2pb557sHnAoB4t2jy95EBK7aB31p049tub3Wre/eUXgAbZ1a0Xv2XmewuGv7Q5\nJm8pZvn4dye/9+OB6vVqKjoaKgptB0C1jLl4wrH5E/N2H/qmn2fOld2rt13IdHpo9v7QzTMf\nb2Bb6eMBJsem86wpL/jp4tYsmPRHkohc++HjNzanVA96aVmwl9KzocLQdgDUyZiwS4/4Y9pj\nXYJ/vy7WNRvUtpOk3bNHBH+w7VJWpU8HmCL7Vu8vH1xPF/fti59tv7jrlVd33HRqN3dZ/9pK\nzwUA0Lwywi7r0t9zBvq36Dtj88Vq7cZ/efh0+JkjP7/c2fHsqjd7NGv95HwungCKUS3w+S/G\n+ciFtcPbzvnpun2PD996tq7SM6GicdAOgAqVEXZnvnh5ypow8Rvw4bbQvUueaeEkDk2Gzt91\nMmTBE031od+/GtDrQ253AtzJvueHbzxd03D9erzdQ+OXj+PNddpE2wFQm7JOxVp6PTTx56PH\nV08O9LYs2Mn9wQnfHzn+x1s9a+kzuEExUAz95YhTcSIi6ecjwpOVngaVhrYDoCpl3e5k8vqd\nHw9tVNznwdrW7zNn68l1o30rZS7ApOmj543+fH+6e5eHausu/P7sGwdTlJ4IlYe2A6AeZd3u\nxM5OV9rjznXqVK/IcQAtMIQvmv3ungz3Ia+u3fDG6DoSufT9t3elKT0VKhFtB0Al7vGzYgHc\nzhC1ZvTb/6U5dfhwXg83x3YfLnrMy3B50eil/5B2mkbbAVADwg6oWFeXPrtoZ4p1lxmTn64l\nIuLa9+V5A53151YFv3s8XenhUKloOwCKU+PnRhjij/+06PMN/0bE6twad+wbPGawf41STwif\n/f39X47fft8Vi+ZD3x7QuBLHBIpzMSqt8xPTuvuNeKl2/t9alxELZ11vefSm1eUz6S1b2Sk6\nHgBA01QXdvoLPwztNOq3S3pbl5puFnGb1nz32WeDvtz2y5MNSjy4eP2vBW+/u/32VcthLQg7\nVL06HSdO73j7Ys12L09vp8Q0qGozDCun6kYpPQUA86W2sLv02VPBv11ye2zehh8mtHXRJZ1c\n8czDz/429v8Wdt79cv0S9omMjBSrHrO3vtOp8KrOs0UVzAsARdF2ABSksrA7+OncnRm2D8/6\n5pW2LiIiTs3HfDbl+7Uv7vhk6cGXPyj+kEd2RMRFqTe8d2BgqyqdFQAAQF3UdfHE6c2bz4uu\n+/ChHgVrnkFBrUQubN58uoSdzkdE5EjDhn5VMiGgWjmn1zzR7bnARxdvTihYO7JgSmDg8yOX\nRPLhfwBgDlQVdmkHDhwXafDAAy6FVxu1bVtd5HRoqKH4vSIiIsXLz8829tSu9b/98tv63aE3\n+DQMmCHLpj2H1b64c/PK8W8dTBUREf3pH8e+/vfOMx7Dh9e3LGNvAIAWqCrsbly7phepVatW\n0WU3NzeRjGvX4ovdKTYiIkEMIW82rn1fQJ/Bwwb36dq8Zv1uk/+4kF0FEwNq4tRv/uRhnhL1\n+Ufv7c8Sw5VF45YfzHQduWTi465KjwYAqBKqeo/dzZs3RcTBwaHosrOzs4ikpxd/D7DIyEiR\n62du9H3lsw+71rOOCd2y7MPPd8wd0C1p039Le5b1uRhRUVEdOnTIysoqZZuMjAwRMRhKOGII\nqIdbwMJFPf4e+vcn474JfO7EO7vSvYZPXdDfWemxAABVRFVhp9PpROSOyspdsLW1LXYnu5aD\nX36t7sC3X+paQ0REHus/akirR1uO37Ls9UWvHn67SelP6evru2LFirS00j4TYOvWrV988UXu\ncIDKeQyZtGDgvyNXf9nneb3eo8dXC7u7KT0SAKDKqCrsXFxcRCQxMVGk8LvsEhMTRWw8PV2K\n3anFyLnzRxZZ0fmOe23Y61u++G/X7uS3mziW+pQWFhZ9+vQpfay4uLgvvvjCiPkBNXB94uOn\nPln96b96XZcpEwa5Kz0OAKAKqeo9drUaNrQTCT93rshqRmTkZZFGTZuWY9batWtJ/jlUwLxk\n7V+y7j8REcO+FWv+K+1dBgAArVFV2Fl07tJJJ3G7dp0otJizZ+eeHPEIDLyvuF2ufD82MLDb\n65tSi6ymnjwZJeLWqFGNSpwWUKPMQyuCP46Sxn3fGOSSfXxl8OyzXEYEAOZDVWEnnoNHBdnJ\nyc9n/x6bt5ITsWz2d1d0fk8/3bXYUT09daE7dyz66MtI/a21rNC5H6xOE+8hwwJ4WxzMS9bZ\nGcErQ3M8xy5+9X+LX+3jknNkzqwP7vggZQCAVqkr7MTjyY/ebW979acnHuw3+aOFn84Y17XT\ni9uSaz6z4O22eZNe/LSnu7t7kzf35P7WsufkaV2d0ra98mDA2Fmff/fjd0tnBT8UOP3fbO8h\n89/rUfzlFoBG5RydM+uD4zmeIybO6WkvXo8s/qBDtayzM4NXniLtAMA8qOriCRGxavnWnxuy\nnxnz4bq5r68TEWvvB1/44dv5vW9dOJGTGh8bGyvJ+e8c0jV84Y+Q6lNfe3fpF++GfCEionPw\n7f7yj599MMxTiRcAKCX7xMpn5pzNrt5p7ieBufet83329Zkrn5gYsiL448A9r9dT2f/GAQAq\nntrCTkTn0X3qn+cmXj5z5kKyrXejxvVcbAo/7P3E59s7JlnXal2wVN1/1PytI9+/cSEs/Eq6\nnUeDpg3dOVQH85Nq3/aTzZ9ZeDXo6p2/pKs1YdWXD5xOMNhbp4qUfoU4KtAMw8qpulFKTwHA\nHKkv7ERExMKxZrM2NYt7xM63TaBvcXvYu9fzd69XuWMBKlbdr0XgHR+ZbOntF+Bd3NYAAC3i\n5AwAVLwZhpVKjwDAHBF2AFApaDsAVY+wA4DKQtsBqGKEHQBUItoOQFUi7ACgctF2AKoMYQcA\nlc502i69q0QHy+WHxHBryUbinpTopyWpuoJzATAOYQcAVcFE2s7uqOh8JKWHxHnlraR3l9jG\nkn1FHBMVnQyAMQg7AKgiJtF2CeK1RSws5GZfydSJwUeudxSJE69twodvAyaAsAMAFGZ1SNyj\nxFBHrreX+H6SoROXNWKfVfaOAJRH2AFA1TGJg3YGcV4r9lmS1ktu1BTr/eJ2XumRABiJsAOA\nKmUSbRcnHgdEdCJZ4vY3PykA08F/rgBQ1dTfdnYS7y8iItaS0FrhWQCUA2EHAApQd9ulPiqJ\nTmK3TxwyJe1hiXdReiAARiLsAJiP5D1fLJ8+ffkXe5IK1rIif5m9fPp7a/+5WdXTqLXt9H5y\n7QGR6+K5STy3i85GYvtJttJTATAKYQfAfDje53358/eWjx2x6O/k3BV96NyZT76zfFl4jftc\nFRhIhW2Xm3EGcflDbPVivVdqXMlPPQDqR9gBMCOuj7+yeEQNubju+WnHMkQM4b+OnRma5RW0\ndH5Xpc42qqztck+8Wv2XfyWsXlzXiY0+7+QsALUj7ACYleoDP5082MNwUzeLygAAIABJREFU\ndsEH7x+5vOy5pXvSXJ/4bGLfGkrPpRaWJ6X2V1J7Y8FPB90lqbVMav8ottyhGFA/wg6AmXHv\ntnhhd7ec8P89MvqNramewyZ/OlDhawPUdNDOJkrsI8U6o8ii1WWxjxRbPlIMUD/CDoDZ8Rw2\n6eM+jhnXbya4dv10YXc3pecRdbUdABNG2AEwPxlXT5xLFRFJij55US2flUXbAbh3hB0Ac5N1\nYPqseaelaVd/j+yI/wV/dVQtaUfbAbhXhB0A85J5+KvRcyNy6vZfuvHDef2rZx39Nvh/59Rz\nlzbaDsC9IOwAmJPsc7ODvz2R7frUp88FOLiMXPhSkFP24Vmz5p7UKz1ZAdoOwF0j7ACYD/2x\n92e9fzTbtd/LH/V1EhGp/fiS2ffbZ55+L/i70zlKT1cIbQfg7lgpPQAAVJWci2FWXd6eFvTg\n6Ec989cavDDlh9RNR9J0ZyL0TRup6P91ZxhWTtWNUnoKACaGsANgNizrDnprzKDbFi1q939j\nTH9F5gGAiqai/z0FABTGCVkA5UXYAYB60XYAyoWwAwBVo+0AGI+wAwC1o+0AGImwAwATQNsB\nMAZhBwCmgbYDUCbCDgBMBm0HoHSEHQAAgEYQdgBgSjhoB6AUhB0AmBjaDkBJCDsAMD20HYBi\nEXYAYJSca+E7dxzese9SUqHFzEtnd+w4vPN4bE6Vz0PbAbgTYQcARrG0vbr8iee7PTj+tS2p\neUs5kR/0De7W7d0vo2wslRiJtgNwG8IOAIzj0nn+Z494Sczy55fuSRcRQ9iC92cfzvYe+fr8\nx52UGoq2A1AYYQcAxnLrP3HRMFdD+K/jZ53OurB23NRjGV4PL1kQ4KroVLQdgFsIOwAwnvPg\nhZMGuutPfDSr57DPtqe4DF/8Wn83pYei7QDkI+wAoDw8eixeEOiaeW7XviSPIZMXDnJReiAA\nKEDYAUD5uDSo5S4iovPwq+ms9DC3cNAOgBB2AFA+GaemBf8YZunq6WYInTtr9n/ZSg9UgLYD\nQNgBgPGy/5056+NT+gbPzzm4uHuN7PA5wV8fV1Ha0XaAuSPsAMBYWUe+Dv4gPMen96JZ9/sO\nm/jRY455K0oPVhhtB5gzwg4AjJMdPif462PZToPnvfRYdRFxf+az5wMcsg/NnPXxKb3SwxVB\n2wFmi7ADAKPEbtrwT/WW3cZMmj8s70pYXb0Bn897NLCj3fZvDyQoOhsA5LJSegAAMA1ufV7a\n3Oe2NV2TsdO3j1VkHAAoBkfsAAAANIKwAwAA0AjCDgAAQCMIOwAAAI0g7AAAADSCsAMAANAI\nwg4AAEAjCDsAAACNIOwAAAA0grADAADQCMIOAABAIwg7ANCgGYaVSo8AQAGEHQBoE20HmCHC\nDgA0i7YDzA1hBwBaRtsBZoWwAwCNo+0A82Gl9ADFMMQf/2nR5xv+jYjVuTXu2Dd4zGD/GroK\n3wUAAEBjVBd2+gs/DO30/+3dd3xN9//A8feNbCuRgVANGVbs2Cqhmi+qqFGtVilqa9DaNb9G\nVX622NTXaBtViqotqNaoXaotCUnMSJEQIuP+/qAkbURE7j0nn/t6/pdPzol387iP9JXPOeem\n09pLaXZOHi5Wf21ZtzI0tO3SXWHvlXnq5mIOTgEAizLeuGK0oZPWUwAwOb2lz6XQ97uuveTS\nbPrhq3GXLt24fmpRW9eLa3t0nh2Zm6cAgMXhgixgCXQWdodnhexJsnttwvIB/k5WIoaCFbuH\njgzMd+/HafMP594pAGCRaDtAefoKu7Nbt14UQ+O333J7suYeFFRFJGrr1rO5dQoAWCzaDlCb\nrsLu3qFDp0TKVK/ulH7Vx9+/kMjZM2eMuXMKAFg02g5QmK7C7sa1a2kiJUqUyLjs4uIiknTt\n2q3cOQUALB1tB6hKV0/F3rx5U0QcHR0zLhcuXFhE7t+/nzunZBAdHR0UFPTgwYMsjomPjxcR\no5HtPwDq4DlZQEm6CjuDwSAiycnJGZcfLtjZ2eXOKRkULVp02LBhSUlJWRyzd+/eVatWPfyX\nAEAZtB2gHl2FnZOTkzzaIEt/y1x8fLyIrbu7U+6ckoGtrW3nzp2zPsZoNK5atSob8wMAAGhJ\nV/fYlfD2thc5f+5chtWkyMjLIj7lymU2aw5OAQA8ws12gGJ0VT5W9RvUM8hfe/f+mm4xdf+e\n/aniFhhYIZdOAQA8QdsBKtFV2Il7u05B9nJ6wcTv4h6tpEYsnLjyisGrS5eGmY+ag1MAAOnR\ndoAydJY+bu9NHVXL7upXHeu2Gjx19qzxPRvW67frjscHM0f4P5o0elYTV1fXssP2Z/8UAMAz\n0HaAGnT18ISIWFcavmlzygfdP98QMmSDiNgUq9t39f9mvP74KYjUxFtxcXFyJzn7pwAAno2H\nZAEF6C3sRAxujUdvOjfo8u+/R92xK+bj6+lkm/7TxTou2F0nwaZE1eyfAgDIFtoOyOv0F3Yi\nImJVwKN8DY/MPmNfqkZgqec7BQCQXbQdkKdxGxoAAIAiCDsAQAY8SAHkXYQdAOCfaDsgjyLs\nAACZoO2AvIiwAwBkjrYD8hzCDgDwVLQdkLcQdgCArNB2QB5C2AEAnoG2A/IKwg4A8Gy0HZAn\nEHYAAACKIOwAANnCph2gf4QdACC7aDtA5wg7AMBzoO0APSPsAADPh7YDdIuwAwA8N9oO0CfC\nDgCQE7QdoEOEHQAgh2g7QG8IOwBAztF2gK4QdgAAAIog7AAAL4RNO0A/CDsAwIui7QCdIOwA\nALmAtgP0gLADAOQO2g7QHGEHAMg1tB2gLcIOAJCbaDtAQ4QdACCX0XaAVgg7AAAARRB2AIDc\nx6YdoAnCDgBgErQdYH6EHQAAgCIIOwAAAEUQdgAAAIqw1noAAAAALcQe37jnXFI2D3ar1jLA\ny9ak8+QGwg4AAFik04s/aD83LpsHB8yODe/natJ5cgNhBwAALFK9sXu2Vl08adTMPVeNUrJJ\nnw5VHJ5+sFc1R/NNlnOEHQAAsEi2rhWDuk8P9E3yCpgX49V2XEgv/e/IPQsPTwDQtdSzK2vb\n1zHYd5v2R9rfa/FrOjQ1GF6pMyUyLatTASAbbBu2beGm9RC5hh07ALqWr1zHpWN2VR9xenTv\n9e13tnlJ5PYPs4LDbtn591r6SWl+NwUsx+TJkxctWpTFAdbW1t98803JkiWf9ytXatCs4j6r\nIko0kRL/EQBUZlVx8MiRa7qM2RXaf2XA+jZRw/psumJbdtKyThXyaT0aALOwtbUWkXbt2vn6\n+mZxmLW1tZtbTvbe3N9d/uu7OZxNbwg7ALpn7TV8aee1NRd/NyhkxJ6IBResq48fNdiPrAMs\nS5s2berVq6f1FHrHdQwAeYBN1S5Lhnrli909efFF66pdlg3z5rdSAPg3wg5AnmDt37VZVRER\nQ633W1S20XocZM944wqtRwCe37XQQGtr61dDs/sWd3pC2AHIE+KWBy8/IlZWVsb9E2eEXdd6\nHAAKM6alpKampqYZtR4kBwg7AHnA1dVTB25KKBj0yYbRvtZx4f3778yLv0lbJjbtAHMi7ADo\nXuzOvsHhN+0qjZ/75uvDhw0sZ3U9LOSjdbe1HgvZRdsBZkPYAdC522v6hXx7w6rq8CH9vQ1i\nW2Hsgnaehpur+0zbdFPr0ZBttB3yEisHJxcXl8IOeTGS8uLMACxI3Ppp/cJuGrw7zBvm8/AN\nThwb9prX1V2ubu018Ed27fIQ2g55hnu3TTdu3PiuWxGtB8kB3jEAgK65tB53zTgu45pj08Ub\njIu1mQcvYrxxxWhDJ62nAFTGjh0AwHzYtwNMirADAJgVbQeYDmEHADA32g4wEcIOAABAEYQd\nAEADbNoBpkDYAQC0QdsBuY6wAwBohrYDchdhBwDQEm0H5CLCDgCgMdoOyC2EHQBAe7QdkCsI\nOwCALtB2wIsj7AAAABRB2AEA9IJNO+AFEXYAAB2h7YAXQdgBAPSFtgNyjLADAOgObQfkDGEH\nANAj2g7IAcIOAKBTtB3wvKy1HiATxlunvpqzYPORiDiDi2+dll27t6tcxJDVCX98NznsVOo/\nFq0qvjXiTV8TjgkAMLnxxhWjDZ20ngLIM3QXdmlRq9+q12ntpTQ7Jw8Xq7+2rFsZGtp26a6w\n98o8dXPx+o6ZI0bt/udqvg5+hB0A5H20HZB9egu7S6Hvd117yaXZ9M2rP/J3MiScXvLBax+u\n7dF5dv19waWfck5kZKRYvzpx+6f10q8a3P3MMC8AAIBu6CzsDs8K2ZNk99qE5QP8nUREClbs\nHjpy1fp+4dPmHw6eUjPTc1IiIqLF8+3XAwOrmHVWAICZsGkHZJO+Hp44u3XrRTE0fvsttydr\n7kFBVUSitm49+5STLkZEpIq3t5dZJgQAaIIHKYDs0FXY3Tt06JRImerVndKv+vj7FxI5e+aM\nMfOzIiIipaiXl13cb3u/Xxu29vt9Z248MMe0AACzou2AZ9JV2N24di1NpESJEhmXXVxcRJKu\nXbuV6UlxERG3xfjjMN+SFQJatOvQrkXDih6lGw3eGJVihokBAOZE2wFZ09U9djdv3hQRR0fH\njMuFCxcWkfv372d6UmRkpMj132+0HBD6eUNPm9gz2xZ+viA85M1GCVuOzW9S6Bn/5OXLl996\n662nfe2HYmNjRcRofMqOIQDAjLjfDsiCZmH3y8Jei48+/qjwq4OntPcyGAwikpycnPHQhwt2\ndnaZfiH7Su2CP365zYj+DYuIiEiz1p3aV2laqde2hUPmDDw6omzWYzg7O7dt2/bBg6wu3h48\neDAqKurhcAAAzdF2wNNoFnbnti1YsPbxR0Xt35vS3svJyUlE4uPjRdLfZRcfHy9i6+7u9K8v\nIiLi927IjHczrBhK9fy4w5Bti47t3XdnRNkCWY7h4OAwcODArEddsGDBunXrsj4GAGBOtB2Q\nKc3CrvG43bv7Pf7ItmQlESnh7W0vh86fOydS6smRSZGRl0XKlSv3HPcDlixZQiQ+KSlJJOuw\nAwAAUIZmYedeMdD9n2tW9RvUM6zetXfvr9L48bsLp+7fsz9V3AIDK2T2Za6s6vHOoj9rDfv+\n86bp7sxLPH36goiLj08RE0wOANADNu2Af9PVU7Hi3q5TkL2cXjDxu7hHK6kRCyeuvGLw6tKl\nYaajursbzuwJnzN1aWTa47XkMyFTvr0nxdp3COC2OABQGA/JAv+gr7ATt/emjqpld/WrjnVb\nDZ46e9b4ng3r9dt1x+ODmSP8H00aPauJq6tr2WH7H36Yr8ngMQ0L3ts1oG5AjwkLVn65cv6E\nrq8Ejj2SUqz9jHGvZv64BQBAGbQdkJ6u3u5ERKwrDd+0OeWD7p9vCBmyQURsitXtu/p/M15/\n/OBEauKtuLg4ufP3k7MG774bfyw0+uNR8xeN+nGRiIjBsVTj4C9Dp3T416VeAAAAlekt7EQM\nbo1Hbzo36PLvv0fdsSvm4+vpZJv+08U6LthdJ8GmRNUnS4Uqd5qx/d3JN6L+PH/lvr1bmXLe\nrmzVAQAAy6O/sBMREasCHuVreGT2GftSNQJLZbJu5eDqWdnV07RjAQAA6JjO7rEDAABAThF2\nAAAAiiDsAAAAFEHYAQAAKIKwAwAAUARhBwAAoAjCDgBM5v7pya17BwYOnnLgweO1u3uWtAjs\n/WrPrZc0HAyAogg7ADAZ+4rvvWF3dM++T3t+cTJFRESSTo/useT7fbHV3g8sofFwABRE2AGA\nCb3UbfjnTRxTTq7oOf2iUVKPTZw88w+jd/9P/1ufv5ADIPcRdgBgUkV7LuoXkD/5wNgpoT+s\n+nDKubQy7ZZOquqg9VgAlETYAYBpGTzfXDypmkPi0Y9azD+SXLzfkj6vOGo9k1rGG1doPQKg\nF4QdAJiawbtfcN8ykpaW5tCq18RAdutyH20HPETYAYDJ3d66dnWEiMi9beuWnzdqPY6aaDtA\nCDsAMLn4Q4N6brxsW+GjQTXzJx4f/uE3F0g706DtAMIOAEzq3o4hk5ZGW/kNGfp/IUPH1bO9\nszu0x8KrWk+lLNoOFo6wAwATuhse+uHCq4YybeeNKGttKDlgYddqNve2D5m0NEbrydRF28GS\nEXYAYDKJJ4Z1/+aC0fWDOb0aOIiI5Kv43sLBXvniD33cc+NlradTGG0Hi2Wt9QAAoK57Tu0X\nz21r5169bv6/l6z9R007+NqlBMmfliTCuxSbzHjjitGGTlpPAZgbYQcAJuPycsPAl/+5aF+0\nRmBRLaYBoD4uxQIA1MQFWVggwg4AoCzaDpaGsAMAqIy2g0Uh7AAAiqPtYDkIOwCA+mg7WAjC\nDgBgEWg7WALCDgBgKWg7KI+wAwAAUARhBwCwIGzaQW2EHQDAstB2UBhhBwCwOLQdVEXYAQAs\nEW0HJRF2AAALRdtBPYQdAMBy0XZQDGEHALBotB1UQtgBACwdbQdlEHYAAACKIOwAAGDTDoog\n7AAAEKHtoARrrQcAoAFjwuV9Ww4dOX87Ob+rX0C9oMrO/CwARGS8ccVoQyetpwByjh/mgKUx\nXtk8t03n1QdupP29Yu/Tvm/Y0vZVC2g5FqATtB3yNC7FApYl+eTy199cedDGf+w3S/+M2Rhx\nbMaMTsWj1/xfUKetV7WeDdAJrski7yLsAItyJ2zM8mMPnLstmzqmbQXvEm6lq9YJXj59Uv18\nsevnzzySyQmpZ1fWtq9jsO827Y/HO3zxazo0NRheqTMlMi2TMwAV0HbIowg7wJIkH9m45Z54\nNu0RZPdk0VDs3Y5VRa7s2nX532fkK9dx6ZgKtkmnR/deHy0iIrd/mBUcdsvOv9vST0rzEwQK\no+2QF/FjGbAkl2LO3RcpX6aCIcOye6li9iJXr8Zldo5VxcEjR1azubsrtP/KOEk8NqzPpiu2\nZccs61Qhn1lmBrRD2yHPIewAS/Ig+YGIwc7WNuNy8p3EJBE7O9vMz7L2Gr60c2XrO98NChkR\n/NmCC9bVPx012I+sAwDdIewAS1LMzcMgxvMxkRmXz5yONIrBx6fE086zqdplyVCvfLG7Jy++\naF21y7Jh3jxRDwvBph3yFsIOsCSFarxa00pO/fDF0XSPPaSc+d+XF8S66htNs3i/E2v/rs2q\niogYar3forKNiecE9IS2Qx5C2AEWpVj3Uc2KS0zI26Nnb4+88lf8lbNH5nYeO/u8oUzvDzsX\nz+LEuOXBy4+IlZWVcf/EGWHXzTYwoAu0HfIKwg6wLM4tBm+eHegRteOjoHc8XII8yvfttzrW\n+92RP4RUd3j6WVdXTx24KaFg0CcbRvtax4X3778z0+csAIXRdsgTuE8GsDT2Vft99nub37Zs\nOXn2apKNc9FKDWs3quiU1c+C2J19g8Nv2lWaPvfN10uVG/hV96lhIR+97b/qzcJmGxrQA/4o\nBfSPsAMskZ1H+VZdy7fK1rG31/QL+faGVdWxQ/p7G0QqjF3Qbk1g2Oo+094JHNfC2cSDAjpD\n20HnuBQLICtx66f1C7tp8O4wb5jPwzc4cWzYa15Xd7m6tdfAH29rPB2gAa7JQs/YsQOQFZfW\n464Zx2Vcc2y6eINxsTbzAACywI4dAADPh0076BZhBwDAc6PtoE+EHQAAOUHbQYcIOwAAcoi2\ng94QdgAA5BxtB10h7AAAeCG0HfSDsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYA\nAACKIOwAAAAUYa31AFm4vG3GwpO+XT5p7pmNg+9f+HHTziMRcQYX3zrNmtXysDP1dAAAADqj\n47CLChs9aNyFPoHPDrv7J2e0fX3o5pgHjz62fumNkA1fBlfNb+IJAQAA9ESnl2JT436Z3mvy\nQWN2jk3c0r/5oM1XS7YN2Xz0jz9ObA/t5HNt44CWwT/Em3pKAAAAPdFd2P227IOg2j5uxWsO\n+uF6tk64uGjcF5ekwpB1X33crJqPT+Umvb8IG1xeopeNWXzBtKMCAADoiu7C7s6VyMt37Tx8\nK1Ys5WTIxvFXN3x7IEVqd+1R+fFVZSu/Vm+UkbTD3228YsJBAQAAdEZ3YVdzRPivD81tZfvs\nw1P2/3RYpHjdui+nX61ev76DyPFjx0w1JQAAgP7oLuyeU2xU1D0RT0/PDKv5ihZ1EYmPieE2\nOwCAGYw3rtB6BEBE10/FZsvNmzdFpGDBghmXnZ2dRWISExNFCmV5/vXr14ODg1NTU7M4JiIi\n4oXnBAAobrxxxWhDJ62ngKXTLOyi9n/1U/TjjxzKNmlVzTUHXyY5OVlEDIZMb8eztn7mf56D\ng4OXl1dKSkoWx1hZWR05csTW1iYH8wEALAdtB81pFnY/TX/nnbWPPyoavK9VtQY5+DIFChQQ\nkfj4eJEC6Zbv3r0rYuXsXPhZ5xcsWHDChAnPGPWnn77++uscDAcAsDS0HbSlWdj5vTVmjN/j\njwrUKZWzL/OSp6eVHI+JiRHxeLJqjIm5LFKyTBk22QAAZkbbQUMaht1Yv2cf9Uy2/v6VZf3x\ngwcvS60nZXfq8OH7Yl+vXrVc+BcAAADyiLz+VKyUbdvOzyA/Lll45vHzD4nhoct/k0Kt325m\nr+VkAABLxUOy0EqeC7vY9UPbtWvXdcnpvxfK9flvx2JpJya2fmf694dPndz75bDXOyyIsq0z\nalxLRy0HBQBYMtoOmshzb3dy9+zOtWuPuBTr93jFufXc9ROvtBq1ZlCLNQ9XClTu/fXaQb7Z\n+cMVAACYCDfbwfx0HHa+rT8d42lfyzPjqlODHmPGXHbMsFy49oid5zvs3rDt6MU7dsUqNHyj\nWWWXPLcVCQBQD20HM9N32I1t/a9VpwY9xmb2vij5vRq907uR6acCAOB50HYwJza2AAAwLe63\ng9kQdgAAmBxtB/Mg7AAAABRB2AEAYA5s2sEMCDsAAMyEtoOpEXYAAJgPbQeTIuwAADAr2g6m\nQ9gBAGButB1MhLADAEADtB1MgbADAEAbtB1yHWEHAIBmaDvkLsIOAABAEYQdAABaYtMOuYiw\nAwBAY2OSlmk9AhRB2AEAACiCsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYAAACK\nIOwAwCw6jxdDHek64cnKqfNiU188WsitBO3GAqAUwg4AzGLGQCnmIss2yd5jIiJpadJjsqSk\nyvyh4lRQ6+EAKIKwAwCzcC4ocweLiPSaIg+SZd63cuBX6fgfafmK1pMBUAdhBwDm0iZQ2jWW\n3y7Ix7NkxDxxd5ZZg7SeCYBSCDsAMKM5n0iRQjJnjcTflbmDxaWw1gMBUIrBaDRqPYPe/fLL\nLzVr1tR6CgCA4g4fPuzv76/1FCIiKSkp9vb2qampWg+SgX6+P3pG2GXLiRMnUlJStJ7CsvTp\n08fd3b1Dhw5aD2JxPv7445YtWwYEBGg9iGVJS0vr3LnzqFGjfH19tZ7Fsly6dGnYsGHbtm0r\nUqSItpNYW1tXqVJF2xnS+/PPP+Pj47We4gm9fX90i7CDTjVv3rxy5cqfffaZ1oNYHG9v7+HD\nh3fr1k3rQSxLSkqKjY3Nvn37GjRooPUsluXMmTMVK1a8du2au7u71rMAuYB77AAAABRB2AEA\nACiCsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYAAACKIOwAAAAUQdhBp2xtbW1t\nbbWewhLxndeEwWCwsbHhO29+tra2D7/5Wg8C5A7+pBh06vr1646OjgUKFNB6EIsTHR1drFgx\n/j9nfhEREaVLlzYYDFoPYnEiIiLKlCmj9RRA7iDsAAAAFMGlWAAAAEUQdgAAAIog7AAAABRB\n2AEAACiCsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYAAACKIOwAAAAUQdgBAAAo\ngrADAABQBGGHPMB4/fSe8OOXk7WeQ33GpL8u/nr40PE/riUatZ7F8vA610LK7ejfjh74+fCp\nCzdTtJ4FyA2EHfKAYzPaBDYasOG21nOoLfHEwi41Pdw8K9WqXa1s8aI+zcduv5qm9VAWhde5\nmd0+Ou/9GiXcSlWoUbdercql3Vz9Okz/mW8/8jprrQcAniH10ur/Lv5DpLjWg6jt8qp3/9Nz\n/Y2SjfsPfatygWs/L5u1dFzzJsk//TKxpr3Ws1kEXudmZry4uF3jPjviXf3fG9Kuuvv9C3tW\nL94YNigozv7Ejt5ltJ4OyDmD0cgVF+hS0m/r5ny1+8i+zZvCzycYRQLmxYb3ctV6KkU92PuR\nV8Dsm41m/7qjn6eViMi9/QP9GsyIqj898scBJbUeT2W8zrVh3BdcquGsvxrNPL7tI5+HOxyJ\nPw+p3mDq70U+2HppaZCtxvMBOcalWOhVwp6Zn4yf/eXu8wn87mFqaTuXr4iRIu8M7en5948E\nh/rd3ikrKfu/+iZG09GUx+tcGyc3b46R/C2De/o8vm7lWDf4w1oiN7ZvP6blZMALIuygVy5d\nvot96OioKloPo7hf9+27JfnqN3rFJt1ixYYNi4gcOXCAW8pNide5NqKiokV8/Pzs0i86OTuL\nSEJCgkZDAbmBe+ygVwb7wq4P7+6648jr1KTSfv/9nMhLPj6O6VcNL79cSuT4hQsxIp4aTWYB\neJ1rI2h+TOxMmwIu6ddubd1yUETKlvXVaCggN/CDBLB4t27eNIoUKVIk47Kzs7OIxMfHazIU\nYEp2BV3tCqZfSDw1+92+a/6SQm/0fa+UVlMBuYCwg9ZS7ty4cefJ1T67wkWdHQwazmOB7t69\nKyI2NjYZl+3s7ESE56ugutQr4dP7dh+17vx9h4q9vlr8vpvWAwEvgnvsoLWzIQ2Kp9N+Oe8j\nZW4ODg6SyZ1F9+7dE5FChQppMRNgDsa/fpnX1b98o8HrzttW7br44IF5zdy1ngl4MezYQWv5\nPWsFBBR7/GEVD16U5uZSooS9yI0bNzIuX7lyRcSqVKkS2kwFmFjCL9PfajVky+WUwpU6Tps9\ntX8AP3ygAl7G0FrpLv8L76L1EJbNUKVKJVl9+MiRKAl4cndR4qkt+2LJAAAF30lEQVRTkSKV\n/f15Ry8oKO3cvFavDdodX/S1cSu/GNGEpoMyuBQLoFTz5hVFjn7zTeSTtbhvw3YmS4WWLb20\nmwswlbvfjBi6+1ahxjPCN4+m6qAUwg6A+PUc3LRg6s/jOo3ddy1VJCX2p8/eHvh9YuE3R/Yr\nr/VsQO5L3Pz1pgRDlcHz+pcj6qAYwg6ASPHOi5Z0Kn1v/7iGHoWKuDgVrz98R3zZbl/M7cgD\nglDRyYMH74nx9MTqBf6t7MjDWo8HvAB+V4H+2ZeqERBQoKqHzbMPRY6VbP+/I2XfmLdw3cHz\nN61cfeq16d2zdXkeiDUjXufmk5ZUqGxAgHfmn3Qrmd+80wC5ysCbVAEAAKiBS7EAAACKIOwA\nAAAUQdgBAAAogrADAABQBGEHAACgCMIOAABAEYQdAACAIgg7AAAARRB2AAAAiiDsAAAAFEHY\nAQAAKIKwAwAAUARhBwAAoAjCDgAAQBGEHQAAgCIIOwAAAEUQdgAAAIog7AAAABRB2AEAACiC\nsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYAAACKIOwAAAAUQdgBAAAogrADAABQ\nBGEHAACgCMIOAABAEYQdAACAIqy1HgCAxbgXe+7PC7GJ+Yp4lvMt5mjQehwAUA87dgBMLyV6\n4/CmZdyL+lSpVa9ujXLFi5QKHPBtZIrWYwGAagxGo1HrGQCo7e6eAdUbz/zDzus/XTsFednd\nOLFhyYqfr0uZPjtPzA0soPV0AKAQwg6Aid1Y9GrxHrtKfrjj+MJXC4uISNqlpS39un0fX/f/\nzv00qLTG4wGAQrgUC+B5JMUcDQ8PDz8SfT/d4t0Lh8LDw/ed/SuzMxK3bt6TIlW7f/yo6kTE\nqkTX/u0KStqB7bsSTD4xAFgQwg7A87CzOvZ560aNajUdfzj50dL9vSOa1Gn0aq/1cY6ZnXEp\nKipVbP38fDOsOjs7iRgTEu6aemAAsCSEHYDn4tFtQUiTgmlnQnqGnE4VkQe/jO8557zBu/+S\nCfXtMzuhTPCO2Ngr85unfwo27fSW7dEizmXLuptnagCwDNxjB+C5XZj/ml/vHWkNpv+6q8mK\nWtXHnnhpwJ5T01/JdMPu39Ku/DDgP21mn3rgM/zAmUk1edMlAMg1hB2A52eMnN2o0kd7DLUb\n+hzfe7xkv10nZwdmK+vu/LZqZLfg2T/Hift/Zm7f0L+yralHBQBLQtgByIm0c7MaVg7ef08M\npXvvOhUamP+ZZyRFbJzQu+/n26If2LwUNHLJ0k9fK5HPDIMCgCXhHjsAOWHl6lW6sIiIXXGv\nl565WZca/W2f2lVaTth21e3VT1afOL11DFUHACbAjh2AHIj/oZtf86Wx7u6216+nBM4+tatf\nmaf/ibD4HX39m4b+aefXJfTLWZ39CppxTgCwLOzYAXhuCTuG9FwabVNt+M79k15xTAwf3n3h\nxaf/inh6RvC8P8Wrx/q9y6g6ADApwg7Ac7qze/CHC6OtfAfNG+rn3XvBmNq2d3YP+XBh9KNP\nJxwNmzNnzpK9lx59fCrs6zPGQm+HTHvNWauJAcBSEHYAnkti+PAPF14wluoxd3RtOxGr8oMW\nDqtiHb99SM+lMSIiErft8/79+w8N+/Ph8XcPHjwjcmfNu0UL/Nuby3mDYgDIRbyDFIDnEb1u\n5emSDYPeHDqpyaNHJqwrj1g46eSQ729uXHmo47Ba9valagQEFCjs4/Tw03HWxQMCAp7y1Xxc\n+eUSAHIRD08AAAAogt+WAQAAFEHYAQAAKIKwAwAAUARhBwAAoAjCDgAAQBGEHQAAgCIIOwAA\nAEUQdgAAAIog7AAAABRB2AEAACiCsAMAAFAEYQcAAKAIwg4AAEARhB0AAIAiCDsAAABFEHYA\nAACKIOwAAAAUQdgBAAAogrADAABQBGEHAACgCMIOAABAEYQdAACAIgg7AAAARRB2AAAAiiDs\nAAAAFEHYAQAAKIKwAwAAUARhBwAAoAjCDgAAQBGEHQAAgCL+H+T73yed76nOAAAAAElFTkSu\nQmCC",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"svmfit=svm(y~., data=dat, kernel=\"linear\", cost=0.1,scale=FALSE)\n",
"plot(svmfit, dat)\n",
"svmfit$index"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that a smaller value of the cost parameter is being used, we obtain a\n",
"larger number of support vectors, because the margin is now wider. Unfortunately, the svm() function does not explicitly output the coefficients of\n",
"the linear decision boundary obtained when the support vector classifier is\n",
"fit, nor does it output the width of the margin.\n",
"The e1071 library includes a built-in function, tune() , to perform cross-validation. By default, tune() performs ten-fold cross-validation on a set\n",
"of models of interest. In order to use this function, we pass in relevant\n",
"information about the set of models that are under consideration. The\n",
"following command indicates that we want to compare SVMs with a linear\n",
"kernel, using a range of values of the cost parameter."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Parameter tuning of ‘svm’:\n",
"\n",
"- sampling method: 10-fold cross validation \n",
"\n",
"- best parameters:\n",
" cost\n",
" 0.1\n",
"\n",
"- best performance: 0.05 \n",
"\n",
"- Detailed performance results:\n",
" cost error dispersion\n",
"1 1e-03 0.55 0.4377975\n",
"2 1e-02 0.55 0.4377975\n",
"3 1e-01 0.05 0.1581139\n",
"4 1e+00 0.15 0.2415229\n",
"5 5e+00 0.15 0.2415229\n",
"6 1e+01 0.15 0.2415229\n",
"7 1e+02 0.15 0.2415229\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"set.seed(1)\n",
"tune.out=tune(svm,y~.,data=dat,kernel=\"linear\",ranges=list(cost=c(0.001, 0.01, 0.1, 1,5,10,100)))\n",
"summary(tune.out)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that cost=0.1 results in the lowest cross-validation error rate. The\n",
"tune() function stores the best model obtained, which can be accessed as\n",
"follows:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"best.tune(method = svm, train.x = y ~ ., data = dat, ranges = list(cost = c(0.001, \n",
" 0.01, 0.1, 1, 5, 10, 100)), kernel = \"linear\")\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: linear \n",
" cost: 0.1 \n",
"\n",
"Number of Support Vectors: 16\n",
"\n",
" ( 8 8 )\n",
"\n",
"\n",
"Number of Classes: 2 \n",
"\n",
"Levels: \n",
" -1 1\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bestmod=tune.out$best.model\n",
"summary(bestmod)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The predict() function can be used to predict the class label on a set of\n",
"test observations, at any given value of the cost parameter. We begin by\n",
"generating a test data set."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"xtest=matrix(rnorm(20*2), ncol=2)\n",
"ytest=sample(c(-1,1), 20, rep=TRUE)\n",
"xtest[ytest==1,]=xtest[ytest==1,] + 1\n",
"testdat=data.frame(x=xtest, y=as.factor(ytest))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we predict the class labels of these test observations. Here we use the\n",
"best model obtained through cross-validation in order to make predictions."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" truth\n",
"predict -1 1\n",
" -1 9 1\n",
" 1 2 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ypred=predict(bestmod,testdat)\n",
"table(predict=ypred, truth=testdat$y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus, with this value of cost, 17 of the test observations are correctly\n",
"classified. What if we had instead used cost=0.01?"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" truth\n",
"predict -1 1\n",
" -1 11 6\n",
" 1 0 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"svmfit=svm(y~., data=dat, kernel=\"linear\", cost=.01,scale=FALSE)\n",
"ypred=predict(svmfit,testdat)\n",
"table(predict=ypred, truth=testdat$y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case 3 additional observation is misclassified.\n",
"\n",
"Now consider a situation in which the two classes are linearly separable.\n",
"Then we can find a separating hyperplane using the svm() function. We\n",
"first further separate the two classes in our simulated data so that they are\n",
"linearly separable:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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Y1HnnjPuEUVni3//LE/7Tjw2tX8lAUAADVjFWGXWvDhsON6dd3tkv/MWPGLy2Wz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\n2wAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"x[y==1,]=x[y==1,]+0.5\n",
"plot(x, col=(y+5)/2, pch=19)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now the observations are just barely linearly separable. We fit the support\n",
"vector classifier and plot the resulting hyperplane, using a very large value\n",
"of cost so that no observations are misclassified."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 1e+05)\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: linear \n",
" cost: 1e+05 \n",
"\n",
"Number of Support Vectors: 3\n",
"\n",
" ( 1 2 )\n",
"\n",
"\n",
"Number of Classes: 2 \n",
"\n",
"Levels: \n",
" -1 1\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dat=data.frame(x=x,y=as.factor(y))\n",
"svmfit=svm(y~., data=dat, kernel=\"linear\", cost=1e5)\n",
"summary(svmfit)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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fflXUJCmhe6mXGBAZRJFDuYjcctI+7M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\nRK5CYII=",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(svmfit, dat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"No training errors were made and only three support vectors were used.\n",
"However, we can see from the figure that the margin is very narrow (because\n",
"the observations that are not support vectors, indicated as circles, are very\n",
"close to the decision boundary). It seems likely that this model will perform\n",
"poorly on test data. We now try a smaller value of cost:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 1)\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: linear \n",
" cost: 1 \n",
"\n",
"Number of Support Vectors: 7\n",
"\n",
" ( 4 3 )\n",
"\n",
"\n",
"Number of Classes: 2 \n",
"\n",
"Levels: \n",
" -1 1\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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SHO6QdXPHfz2Gd/nTXuqWv3vXSF7Wmjo6Pl0v8/Kx/vWXTVEtK+WkbGBaDtAACo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"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"svmfit=svm(y~., data=dat, kernel=\"linear\", cost=1)\n",
"summary(svmfit)\n",
"plot(svmfit,dat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Support Vector Machine"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to fit an SVM using a non-linear kernel, we once again use the svm()\n",
"function. However, now we use a different value of the parameter kernel .\n",
"To fit an SVM with a polynomial kernel we use kernel=\"polynomial\" , and\n",
"to fit an SVM with a radial kernel we use kernel=\"radial\" . In the former\n",
"case we also use the degree argument to specify a degree for the polynomial\n",
"kernel, and in the latter case we use gamma to specify a\n",
"value of γ for the radial basis kernel.\n",
"We first generate some data with a non-linear class boundary, as follows:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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KPR2twkJCTU3NzcxXl4moaGBnfvh+4G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\nrkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"set.seed(1)\n",
"x=matrix(rnorm(200*2), ncol=2)\n",
"x[1:100,]=x[1:100,]+2\n",
"x[101:150,]=x[101:150,]-2\n",
"y=c(rep(1,150),rep(2,50))\n",
"dat=data.frame(x=x,y=as.factor(y))\n",
"plot(x, col=y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data is randomly split into training and testing groups. We then fit\n",
"the training data using the svm() function with a radial kernel and γ = 1:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"svm(formula = y ~ ., data = dat[train, ], kernel = \"radial\", gamma = 1, \n",
" cost = 1)\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: radial \n",
" cost: 1 \n",
"\n",
"Number of Support Vectors: 31\n",
"\n",
" ( 16 15 )\n",
"\n",
"\n",
"Number of Classes: 2 \n",
"\n",
"Levels: \n",
" 1 2\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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rIdH5NoN2frJ6sPN28GfIzPFpVvbNDTqHcbOfwa/V3m1y8fw1PYUkqtWqvICPO6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\nHBhn7Og2ftY7jDsWNNzp5oIGpXUWNAh5cDsBnz3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gvuvjTwmjEijgpyIR2TN+hJH9ktV5d/J7dRVZmyevNfIAACAASURBVOaM/XHf+yPW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\nTiDaIQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"train=sample(200,100)\n",
"svmfit=svm(y~., data=dat[train,], kernel=\"radial\", gamma=1, cost=1)\n",
"plot(svmfit, dat[train,])\n",
"summary(svmfit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot shows that the resulting SVM has a decidedly non-linear\n",
"boundary.\n",
"\n",
"We can see from the figure that there are a fair number of training errors\n",
"in this SVM fit. If we increase the value of cost, we can reduce the number\n",
"of training errors. However, this comes at the price of a more irregular\n",
"decision boundary that seems to be at risk of overfitting the data."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ygpzvsL03cEZfO7NgCAQgh2AACVyEt1lB20bfqFj9myUw7NNRaXsTq80FQy++3W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SsiGJ2+d0/O6avnafoxEHIu9uefB4/+WV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\nHQAAgEpQ7AAAAFTi/wYp7ku+1SIgAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"svmfit=svm(y~., data=dat[train,], kernel=\"radial\",gamma=1,cost=1e5)\n",
"plot(svmfit,dat[train,])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform cross-validation using tune() to select the best choice of\n",
"γ and cost for an SVM with a radial kernel"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Parameter tuning of ‘svm’:\n",
"\n",
"- sampling method: 10-fold cross validation \n",
"\n",
"- best parameters:\n",
" cost gamma\n",
" 1 0.5\n",
"\n",
"- best performance: 0.07 \n",
"\n",
"- Detailed performance results:\n",
" cost gamma error dispersion\n",
"1 1e-01 0.5 0.26 0.15776213\n",
"2 1e+00 0.5 0.07 0.08232726\n",
"3 1e+01 0.5 0.07 0.08232726\n",
"4 1e+02 0.5 0.14 0.15055453\n",
"5 1e+03 0.5 0.11 0.07378648\n",
"6 1e-01 1.0 0.22 0.16193277\n",
"7 1e+00 1.0 0.07 0.08232726\n",
"8 1e+01 1.0 0.09 0.07378648\n",
"9 1e+02 1.0 0.12 0.12292726\n",
"10 1e+03 1.0 0.11 0.11005049\n",
"11 1e-01 2.0 0.27 0.15670212\n",
"12 1e+00 2.0 0.07 0.08232726\n",
"13 1e+01 2.0 0.11 0.07378648\n",
"14 1e+02 2.0 0.12 0.13165612\n",
"15 1e+03 2.0 0.16 0.13498971\n",
"16 1e-01 3.0 0.27 0.15670212\n",
"17 1e+00 3.0 0.07 0.08232726\n",
"18 1e+01 3.0 0.08 0.07888106\n",
"19 1e+02 3.0 0.13 0.14181365\n",
"20 1e+03 3.0 0.15 0.13540064\n",
"21 1e-01 4.0 0.27 0.15670212\n",
"22 1e+00 4.0 0.07 0.08232726\n",
"23 1e+01 4.0 0.09 0.07378648\n",
"24 1e+02 4.0 0.13 0.14181365\n",
"25 1e+03 4.0 0.15 0.13540064\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"set.seed(1)\n",
"tune.out=tune(svm, y~., data=dat[train,], kernel=\"radial\", ranges=list(cost=c(0.1,1,10,100,1000),gamma=c(0.5,1,2,3,4)))\n",
"summary(tune.out)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore, the best choice of parameters involves cost=1 and gamma=0.5. We\n",
"can view the test set predictions for this model by applying the predict()\n",
"function to the data. Notice that to do this we subset the dataframe dat\n",
"using -train as an index set."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" pred\n",
"true 1 2\n",
" 1 54 23\n",
" 2 17 6"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(true=dat[-train,\"y\"], pred=predict(tune.out$best.model,newx=dat[-train,]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## SVM with Multiple Classes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the response is a factor containing more than two levels, then the svm()\n",
"function will perform multi-class classification using the one-versus-one ap-\n",
"proach. We explore that setting here by generating a third class of observations."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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LEiVq/G+vV48kS6ZKQAix0REf1fZiZW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\n3O35zPszuZFc3kuejpaOvb29tbV1jZOpYuvWrdO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GZ/n6+pbOyRCLP3v2jMPh3Lp1q7r5VLBlyxZFRdrznPoAACAASURBVEUjIyN3d/e2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\nSIKCglq1aiV0lpI4Y0dExaRL0y+lXxplPOrNo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bM/+GXPfy1disRE3LwJY+PCSseOcHFBx46YMgX79r31RA8PjBqFuXNRp06x+qZNkErl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\nX0zZAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"set.seed(1)\n",
"x=rbind(x, matrix(rnorm(50*2), ncol=2))\n",
"y=c(y, rep(0,50))\n",
"x[y==0,2]=x[y==0,2]+2\n",
"dat=data.frame(x=x, y=as.factor(y))\n",
"par(mfrow=c(1,1))\n",
"plot(x,col=(y+1))"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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MBcrefAGsg+Qi9gGMQm4xkA7jnEF2B/TGg4ES0TLflIwU5EmqwYoQexd+BMJDYM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z7Md9Z6xJU+98rvPTxmkmrAwPbjS1a5h+6Lver28HRtUAACAASURBVO92RVSsHgZg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",
"text/plain": [
"Plot with title “SVM classification plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"svmfit=svm(y~., data=dat, kernel=\"radial\", cost=10, gamma=1)\n",
"plot(svmfit, dat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Application to Gene Expression Data (optional)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now examine the Khan data set, which consists of a number of tissue\n",
"samples corresponding to four distinct types of small round blue cell tumors. For each tissue sample, gene expression measurements are available.\n",
"The data set consists of training data, xtrain and ytrain , and testing data,\n",
"xtest and ytest .\n",
"We examine the dimension of the data:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 'xtrain'
\n",
"\t- 'xtest'
\n",
"\t- 'ytrain'
\n",
"\t- 'ytest'
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'xtrain'\n",
"\\item 'xtest'\n",
"\\item 'ytrain'\n",
"\\item 'ytest'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'xtrain'\n",
"2. 'xtest'\n",
"3. 'ytrain'\n",
"4. 'ytest'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"xtrain\" \"xtest\" \"ytrain\" \"ytest\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"library(ISLR)\n",
"names(Khan)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 63
\n",
"\t- 2308
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 63\n",
"\\item 2308\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 63\n",
"2. 2308\n",
"\n",
"\n"
],
"text/plain": [
"[1] 63 2308"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dim(Khan$xtrain)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 20
\n",
"\t- 2308
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 20\n",
"\\item 2308\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 20\n",
"2. 2308\n",
"\n",
"\n"
],
"text/plain": [
"[1] 20 2308"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dim(Khan$xtest)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"63"
],
"text/latex": [
"63"
],
"text/markdown": [
"63"
],
"text/plain": [
"[1] 63"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"length(Khan$ytrain)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"20"
],
"text/latex": [
"20"
],
"text/markdown": [
"20"
],
"text/plain": [
"[1] 20"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"length(Khan$ytest)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This data set consists of expression measurements for 2,308 genes.\n",
"The training and test sets consist of 63 and 20 observations respectively."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 1 2 3 4 \n",
" 8 23 12 20 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(Khan$ytrain)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"1 2 3 4 \n",
"3 6 6 5 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(Khan$ytest)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will use a support vector approach to predict cancer subtype using gene\n",
"expression measurements. In this data set, there are a very large number\n",
"of features relative to the number of observations. This suggests that we\n",
"should use a linear kernel, because the additional flexibility that will result\n",
"from using a polynomial or radial kernel is unnecessary."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 10)\n",
"\n",
"\n",
"Parameters:\n",
" SVM-Type: C-classification \n",
" SVM-Kernel: linear \n",
" cost: 10 \n",
"\n",
"Number of Support Vectors: 58\n",
"\n",
" ( 20 20 11 7 )\n",
"\n",
"\n",
"Number of Classes: 4 \n",
"\n",
"Levels: \n",
" 1 2 3 4\n",
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dat=data.frame(x=Khan$xtrain, y=as.factor(Khan$ytrain))\n",
"out=svm(y~., data=dat, kernel=\"linear\",cost=10)\n",
"summary(out)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" \n",
" 1 2 3 4\n",
" 1 8 0 0 0\n",
" 2 0 23 0 0\n",
" 3 0 0 12 0\n",
" 4 0 0 0 20"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(out$fitted, dat$y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that there are no training errors. In fact, this is not surprising,\n",
"because the large number of variables relative to the number of observations\n",
"implies that it is easy to find hyperplanes that fully separate the classes. We\n",
"are most interested not in the support vector classifier’s performance on the\n",
"training observations, but rather its performance on the test observations."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" \n",
"pred.te 1 2 3 4\n",
" 1 3 0 0 0\n",
" 2 0 6 2 0\n",
" 3 0 0 4 0\n",
" 4 0 0 0 5"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dat.te=data.frame(x=Khan$xtest, y=as.factor(Khan$ytest))\n",
"pred.te=predict(out, newdata=dat.te)\n",
"table(pred.te, dat.te$y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that using cost=10 yields two test set errors on this data."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/src/model_selection.ipynb b/src/model_selection.ipynb
index 42a6c90..98758d6 100644
--- a/src/model_selection.ipynb
+++ b/src/model_selection.ipynb
@@ -1,535 +1,1605 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Working with Notebooks:\n",
"* Press `Shift + Enter` to evaluate a cell.\n",
"* Only the return value of the last line of each cell is shown in the `Out` cells. If you want to see the result of an intermediate step, insert a new cell (with the `+` symbol in the toolbar) and paste that intermediate step to that cell.\n",
"\n",
"New R commands:\n",
"* `regsubsets`: used for subset selection, `method` can be e.g. `\"exhaustive\"` (best subset), `\"forward\"`, `\"backward\"`\n",
"\n",
"Useful R commands to remember:\n",
"* `which.min` and `which.max` return the index that contains the smallest or largest element in a list.\n",
"* `sample(range, number_of_samples, replace = True/False)`\n",
"* `apply(data, i, function)` where `i = 1` if the function should be applied to all rows and `i=2` if the function should be applied to all columns."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The Contrived High-Dimensional Example "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data Set\n",
"First we create an artifical data set with n = 50 points of p = 1000 random predictors and one response that does not depend on the predictors."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 87,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T15:18:03.937719Z",
"start_time": "2019-10-14T15:18:03.836Z"
}
},
"outputs": [],
"source": [
"set.seed(932)\n",
"data = data.frame(matrix(rnorm(50*1000), 50, 1000))\n",
"data$y = rnorm(50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Forward Selection with Adjusted Training Loss\n",
"Now we load the `leaps` package and use the `regsubsets` function to do forward selection up to at most `nvmax = 30` predictors.\n",
"We use the formula `y ~ .` to indicate that the response `y` should be regressed on all other columns of `data`."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 88,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T15:27:04.754554Z",
"start_time": "2019-10-14T15:27:04.295Z"
}
},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Warning message in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in = force.in, :\n",
+ "“951 linear dependencies found”\n"
+ ]
+ }
+ ],
"source": [
"library(leaps)\n",
"regfit.fwd = regsubsets(y ~ .,data = data, method = \"forward\", nvmax = 30)\n",
"regfit.fwd.summary = summary(regfit.fwd)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us plot the adjusted R^2 and mark in red the optimal (maximal) R^2."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 89,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:21:36.439367Z",
"start_time": "2019-10-14T16:21:36.356Z"
}
},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6+/9u7d28LCQnYoAFAsih2A7Je+fcnc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\nAzG5jtoE8S2DAAAAAElFTkSuQmCC",
+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
"source": [
"plot(regfit.fwd.summary$adjr2, type = \"l\", xlab = \"Number of Variables\", ylab = \"adjusted R^2\")\n",
"adjr2.max = which.max(regfit.fwd.summary$adjr2)\n",
"points(adjr2.max, regfit.fwd.summary$adjr2[adjr2.max], col = \"red\", cex = 2, pch = 20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot now the BIC-curve and mark the optimal BIC point in red. Write your answer in the following cell.\n",
"\n",
"Hints: \n",
"1. Use `names(regfit.fwd.summary)` to see how BIC is called in the `regfit.fwd.summary`.\n",
"2. What does optimal mean for the BIC?"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 90,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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HR0QkJCtm3btnr1amdn5wsXLoheBADA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\nTkSuQmCC",
+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot(regfit.fwd.summary$bic, type = \"l\", xlab = \"Number of Variables\", ylab = \"BIC\")\n",
+ "bic.min = which.min(regfit.fwd.summary$bic)\n",
+ "points(bic.min, regfit.fwd.summary$bic[bic.min], col = \"red\", cex = 2, pch = 20)"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Forward Selection with Cross-Validation (the Wrong Way)\n",
"Now we do model selection with cross-validation. But we still use the full data set for training (which is wrong!!!).\n",
"\n",
"Since there is no predict function for regsubsets, we define our own one.\n",
"You don't need to fully understand this code now. If you are motivated to dive in deeper you can have a look at the bottom of this notebook."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T15:42:10.442196Z",
"start_time": "2019-10-14T15:42:10.427Z"
}
},
"outputs": [],
"source": [
"predict.regsubsets = function(object, newdata, id, ...) {\n",
" form = as.formula(object$call[[2]])\n",
" mat = model.matrix(form, newdata)\n",
" coefi = coef(object, id = id)\n",
" xvars = names(coefi)\n",
" mat[,xvars] %*% coefi\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we do 5-fold cross-validation. The variable `folds` will be an array of indices telling us in which of the `k` folds data-point `i` should lie. We will then loop over all folds and all models with 0 to 29 predictors (plus one variable for the intercept) and save the validation errors in the matrix `cv.errors.wrong` where we indicate in the variable name that these are the errors for the wrong cv approach.\n",
"\n",
"The next cell will take some time to run. The star in `[*]` on the left indicates that the cell is still running or in the bottom pane you can see that R is busy."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"k = 5\n",
"folds = sample(1:k, nrow(data), replace = T)\n",
"cv.errors.wrong = matrix(NA, k, 30)\n",
"for (j in 1:k) {\n",
" for (i in 1:30) {\n",
" pred = predict(regfit.fwd, data[folds==j,], id = i)\n",
" cv.errors.wrong[j,i] = mean( (data$y[folds==j] - pred)^2 )\n",
" }\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we average over all columns (folds) to get the mean cv-error for each number of predictors. The `2` in the `apply` function tells that the `mean` should be taken over each column.\n",
"\n",
"Then we plot and include in the plot as a dashed line also the standard deviation of the reponse, which should be a lower bound for our estimated test error."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"mean.cv.errors.wrong = apply(cv.errors.wrong, 2, mean)\n",
"plot(mean.cv.errors.wrong, type = \"l\", ylim = c(0, 1.3), xlab = \"Number of Variables\", ylab = \"5-fold CV wrong\")\n",
"cv.wrong.min = which.min(mean.cv.errors.wrong)\n",
"points(cv.wrong.min, mean.cv.errors.wrong[cv.wrong.min], col = \"red\", cex = 2, pch = 20)\n",
"abline(sd(data$y), 0, lty = \"dashed\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Forward Selection with Cross-Validation (the Right Way)\n",
"The right way is almost the same as the wrong way, except that the training sets in the forward selection are the complements of the validation sets. Compare line 3 in the following cell to the for loop in the above section."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cv.errors = matrix(NA, k, 30)\n",
"for (j in 1:k) {\n",
" regfit.fwd = regsubsets(y ~ ., data = data[folds!=j,], method = \"forward\", nvmax = 30)\n",
" for (i in 1:30) {\n",
" pred = predict(regfit.fwd, data[folds==j,], id = i)\n",
" cv.errors[j,i] = mean( (data$y[folds==j] - pred)^2 )\n",
" }\n",
"}\n",
"mean.cv.errors = apply(cv.errors, 2, mean)\n",
"plot(mean.cv.errors, type = \"l\", ylim = c(1, 3),\n",
" xlab = \"Number of Variables\", ylab = \"5-fold CV right\")\n",
"cv.min = which.min(mean.cv.errors)\n",
"points(cv.min, mean.cv.errors[cv.min], col = \"red\", cex = 2, pch = 20)\n",
"abline(sd(data$y), 0, lty = \"dashed\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model Selection Applied to the Hitters Data\n",
"Here we will apply model section approaches to the Hitters data. We\n",
"wish to predict a baseball player’s Salary on the basis of various statistics\n",
"associated with performance in the previous year. This section follows the Lab 1 in chapter 6 from the textbook.\n",
"\n",
"First of all, we note that the Salary variable is missing for some of the\n",
"players. The `is.na()` function can be used to identify the missing observations. It returns a vector of the same length as the input vector, with a TRUE\n",
"for any elements that are missing, and a FALSE for non-missing elements.\n",
"The `sum()` function can then be used to count all of the missing elements."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 108,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:15:16.280613Z",
"start_time": "2019-10-14T16:15:16.258Z"
}
},
- "outputs": [],
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+ {
+ "data": {
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+ "\n",
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+ "\t- 'Hits'
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+ "\t- 'HmRun'
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+ "\t- 'RBI'
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+ "\t- 'CAtBat'
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+ "\t- 'CHmRun'
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+ "\\begin{enumerate*}\n",
+ "\\item 'AtBat'\n",
+ "\\item 'Hits'\n",
+ "\\item 'HmRun'\n",
+ "\\item 'Runs'\n",
+ "\\item 'RBI'\n",
+ "\\item 'Walks'\n",
+ "\\item 'Years'\n",
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+ "text/markdown": [
+ "1. 'AtBat'\n",
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+ "5. 'RBI'\n",
+ "6. 'Walks'\n",
+ "7. 'Years'\n",
+ "8. 'CAtBat'\n",
+ "9. 'CHits'\n",
+ "10. 'CHmRun'\n",
+ "11. 'CRuns'\n",
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+ "14. 'League'\n",
+ "15. 'Division'\n",
+ "16. 'PutOuts'\n",
+ "17. 'Assists'\n",
+ "18. 'Errors'\n",
+ "19. 'Salary'\n",
+ "20. 'NewLeague'\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ " [1] \"AtBat\" \"Hits\" \"HmRun\" \"Runs\" \"RBI\" \"Walks\" \n",
+ " [7] \"Years\" \"CAtBat\" \"CHits\" \"CHmRun\" \"CRuns\" \"CRBI\" \n",
+ "[13] \"CWalks\" \"League\" \"Division\" \"PutOuts\" \"Assists\" \"Errors\" \n",
+ "[19] \"Salary\" \"NewLeague\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"library(ISLR)\n",
"names(Hitters)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 109,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:15:16.848659Z",
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+ "\\begin{enumerate*}\n",
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"dim(Hitters)"
]
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"cell_type": "code",
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"end_time": "2019-10-14T16:15:17.454300Z",
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+ "\\item 300\n",
+ "\\item 250\n",
+ "\\item 1050\n",
+ "\\item 215\n",
+ "\\item 400\n",
+ "\\item 560\n",
+ "\\item 1670\n",
+ "\\item 487.5\n",
+ "\\item 425\n",
+ "\\item 500\n",
+ "\\item 250\n",
+ "\\item 400\n",
+ "\\item 450\n",
+ "\\item 750\n",
+ "\\item 70\n",
+ "\\item 875\n",
+ "\\item 190\n",
+ "\\item 191\n",
+ "\\item 740\n",
+ "\\item 250\n",
+ "\\item 140\n",
+ "\\item 97.5\n",
+ "\\item 740\n",
+ "\\item 140\n",
+ "\\item 341.667\n",
+ "\\item 1000\n",
+ "\\item 100\n",
+ "\\item 90\n",
+ "\\item 200\n",
+ "\\item 135\n",
+ "\\item 155\n",
+ "\\item 475\n",
+ "\\item 1450\n",
+ "\\item 150\n",
+ "\\item 105\n",
+ "\\item 350\n",
+ "\\item 90\n",
+ "\\item 530\n",
+ "\\item 341.667\n",
+ "\\item 940\n",
+ "\\item 350\n",
+ "\\item 326.667\n",
+ "\\item 250\n",
+ "\\item 740\n",
+ "\\item 425\n",
+ "\\item 925\n",
+ "\\item 185\n",
+ "\\item 920\n",
+ "\\item 286.667\n",
+ "\\item 245\n",
+ "\\item 235\n",
+ "\\item 1150\n",
+ "\\item 160\n",
+ "\\item 425\n",
+ "\\item 900\n",
+ "\\item 500\n",
+ "\\item 277.5\n",
+ "\\item 750\n",
+ "\\item 160\n",
+ "\\item 1300\n",
+ "\\item 525\n",
+ "\\item 550\n",
+ "\\item 1600\n",
+ "\\item 120\n",
+ "\\item 165\n",
+ "\\item 700\n",
+ "\\item 875\n",
+ "\\item 385\n",
+ "\\item 960\n",
+ "\\item 1000\n",
+ "\\end{enumerate*}\n"
+ ],
+ "text/markdown": [
+ "1. 475\n",
+ "2. 480\n",
+ "3. 500\n",
+ "4. 91.5\n",
+ "5. 750\n",
+ "6. 70\n",
+ "7. 100\n",
+ "8. 75\n",
+ "9. 1100\n",
+ "10. 517.143\n",
+ "11. 512.5\n",
+ "12. 550\n",
+ "13. 700\n",
+ "14. 240\n",
+ "15. 775\n",
+ "16. 175\n",
+ "17. 135\n",
+ "18. 100\n",
+ "19. 115\n",
+ "20. 600\n",
+ "21. 776.667\n",
+ "22. 765\n",
+ "23. 708.333\n",
+ "24. 750\n",
+ "25. 625\n",
+ "26. 900\n",
+ "27. 110\n",
+ "28. 612.5\n",
+ "29. 300\n",
+ "30. 850\n",
+ "31. 90\n",
+ "32. 67.5\n",
+ "33. 180\n",
+ "34. 305\n",
+ "35. 215\n",
+ "36. 247.5\n",
+ "37. 815\n",
+ "38. 875\n",
+ "39. 70\n",
+ "40. 1200\n",
+ "41. 675\n",
+ "42. 415\n",
+ "43. 340\n",
+ "44. 416.667\n",
+ "45. 1350\n",
+ "46. 90\n",
+ "47. 275\n",
+ "48. 230\n",
+ "49. 225\n",
+ "50. 950\n",
+ "51. 75\n",
+ "52. 105\n",
+ "53. 320\n",
+ "54. 850\n",
+ "55. 535\n",
+ "56. 933.333\n",
+ "57. 850\n",
+ "58. 210\n",
+ "59. 325\n",
+ "60. 275\n",
+ "61. 450\n",
+ "62. 1975\n",
+ "63. 1900\n",
+ "64. 600\n",
+ "65. 1041.667\n",
+ "66. 110\n",
+ "67. 260\n",
+ "68. 475\n",
+ "69. 431.5\n",
+ "70. 1220\n",
+ "71. 70\n",
+ "72. 145\n",
+ "73. 595\n",
+ "74. 1861.46\n",
+ "75. 300\n",
+ "76. 490\n",
+ "77. 2460\n",
+ "78. 375\n",
+ "79. 750\n",
+ "80. 1175\n",
+ "81. 70\n",
+ "82. 1500\n",
+ "83. 385\n",
+ "84. 1925.571\n",
+ "85. 215\n",
+ "86. 900\n",
+ "87. 155\n",
+ "88. 700\n",
+ "89. 535\n",
+ "90. 362.5\n",
+ "91. 733.333\n",
+ "92. 200\n",
+ "93. 400\n",
+ "94. 400\n",
+ "95. 737.5\n",
+ "96. 500\n",
+ "97. 600\n",
+ "98. 662.5\n",
+ "99. 950\n",
+ "100. 750\n",
+ "101. 297.5\n",
+ "102. 325\n",
+ "103. 87.5\n",
+ "104. 175\n",
+ "105. 90\n",
+ "106. 1237.5\n",
+ "107. 430\n",
+ "108. 100\n",
+ "109. 165\n",
+ "110. 250\n",
+ "111. 1300\n",
+ "112. 773.333\n",
+ "113. 1008.333\n",
+ "114. 275\n",
+ "115. 775\n",
+ "116. 850\n",
+ "117. 365\n",
+ "118. 95\n",
+ "119. 110\n",
+ "120. 100\n",
+ "121. 277.5\n",
+ "122. 80\n",
+ "123. 600\n",
+ "124. 200\n",
+ "125. 657\n",
+ "126. 75\n",
+ "127. 2412.5\n",
+ "128. 250\n",
+ "129. 155\n",
+ "130. 640\n",
+ "131. 300\n",
+ "132. 110\n",
+ "133. 825\n",
+ "134. 195\n",
+ "135. 450\n",
+ "136. 630\n",
+ "137. 86.5\n",
+ "138. 1300\n",
+ "139. 1000\n",
+ "140. 1800\n",
+ "141. 1310\n",
+ "142. 737.5\n",
+ "143. 625\n",
+ "144. 125\n",
+ "145. 1043.333\n",
+ "146. 725\n",
+ "147. 300\n",
+ "148. 365\n",
+ "149. 75\n",
+ "150. 1183.333\n",
+ "151. 202.5\n",
+ "152. 225\n",
+ "153. 525\n",
+ "154. 265\n",
+ "155. 787.5\n",
+ "156. 800\n",
+ "157. 587.5\n",
+ "158. 145\n",
+ "159. 420\n",
+ "160. 75\n",
+ "161. 575\n",
+ "162. 780\n",
+ "163. 90\n",
+ "164. 150\n",
+ "165. 700\n",
+ "166. 550\n",
+ "167. 650\n",
+ "168. 68\n",
+ "169. 100\n",
+ "170. 670\n",
+ "171. 175\n",
+ "172. 137\n",
+ "173. 2127.333\n",
+ "174. 875\n",
+ "175. 120\n",
+ "176. 140\n",
+ "177. 210\n",
+ "178. 800\n",
+ "179. 240\n",
+ "180. 350\n",
+ "181. 175\n",
+ "182. 200\n",
+ "183. 1940\n",
+ "184. 700\n",
+ "185. 750\n",
+ "186. 450\n",
+ "187. 172\n",
+ "188. 1260\n",
+ "189. 750\n",
+ "190. 190\n",
+ "191. 580\n",
+ "192. 130\n",
+ "193. 450\n",
+ "194. 300\n",
+ "195. 250\n",
+ "196. 1050\n",
+ "197. 215\n",
+ "198. 400\n",
+ "199. 560\n",
+ "200. 1670\n",
+ "201. 487.5\n",
+ "202. 425\n",
+ "203. 500\n",
+ "204. 250\n",
+ "205. 400\n",
+ "206. 450\n",
+ "207. 750\n",
+ "208. 70\n",
+ "209. 875\n",
+ "210. 190\n",
+ "211. 191\n",
+ "212. 740\n",
+ "213. 250\n",
+ "214. 140\n",
+ "215. 97.5\n",
+ "216. 740\n",
+ "217. 140\n",
+ "218. 341.667\n",
+ "219. 1000\n",
+ "220. 100\n",
+ "221. 90\n",
+ "222. 200\n",
+ "223. 135\n",
+ "224. 155\n",
+ "225. 475\n",
+ "226. 1450\n",
+ "227. 150\n",
+ "228. 105\n",
+ "229. 350\n",
+ "230. 90\n",
+ "231. 530\n",
+ "232. 341.667\n",
+ "233. 940\n",
+ "234. 350\n",
+ "235. 326.667\n",
+ "236. 250\n",
+ "237. 740\n",
+ "238. 425\n",
+ "239. 925\n",
+ "240. 185\n",
+ "241. 920\n",
+ "242. 286.667\n",
+ "243. 245\n",
+ "244. 235\n",
+ "245. 1150\n",
+ "246. 160\n",
+ "247. 425\n",
+ "248. 900\n",
+ "249. 500\n",
+ "250. 277.5\n",
+ "251. 750\n",
+ "252. 160\n",
+ "253. 1300\n",
+ "254. 525\n",
+ "255. 550\n",
+ "256. 1600\n",
+ "257. 120\n",
+ "258. 165\n",
+ "259. 700\n",
+ "260. 875\n",
+ "261. 385\n",
+ "262. 960\n",
+ "263. 1000\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ " [1] 475.000 480.000 500.000 91.500 750.000 70.000 100.000 75.000\n",
+ " [9] 1100.000 517.143 512.500 550.000 700.000 240.000 775.000 175.000\n",
+ " [17] 135.000 100.000 115.000 600.000 776.667 765.000 708.333 750.000\n",
+ " [25] 625.000 900.000 110.000 612.500 300.000 850.000 90.000 67.500\n",
+ " [33] 180.000 305.000 215.000 247.500 815.000 875.000 70.000 1200.000\n",
+ " [41] 675.000 415.000 340.000 416.667 1350.000 90.000 275.000 230.000\n",
+ " [49] 225.000 950.000 75.000 105.000 320.000 850.000 535.000 933.333\n",
+ " [57] 850.000 210.000 325.000 275.000 450.000 1975.000 1900.000 600.000\n",
+ " [65] 1041.667 110.000 260.000 475.000 431.500 1220.000 70.000 145.000\n",
+ " [73] 595.000 1861.460 300.000 490.000 2460.000 375.000 750.000 1175.000\n",
+ " [81] 70.000 1500.000 385.000 1925.571 215.000 900.000 155.000 700.000\n",
+ " [89] 535.000 362.500 733.333 200.000 400.000 400.000 737.500 500.000\n",
+ " [97] 600.000 662.500 950.000 750.000 297.500 325.000 87.500 175.000\n",
+ "[105] 90.000 1237.500 430.000 100.000 165.000 250.000 1300.000 773.333\n",
+ "[113] 1008.333 275.000 775.000 850.000 365.000 95.000 110.000 100.000\n",
+ "[121] 277.500 80.000 600.000 200.000 657.000 75.000 2412.500 250.000\n",
+ "[129] 155.000 640.000 300.000 110.000 825.000 195.000 450.000 630.000\n",
+ "[137] 86.500 1300.000 1000.000 1800.000 1310.000 737.500 625.000 125.000\n",
+ "[145] 1043.333 725.000 300.000 365.000 75.000 1183.333 202.500 225.000\n",
+ "[153] 525.000 265.000 787.500 800.000 587.500 145.000 420.000 75.000\n",
+ "[161] 575.000 780.000 90.000 150.000 700.000 550.000 650.000 68.000\n",
+ "[169] 100.000 670.000 175.000 137.000 2127.333 875.000 120.000 140.000\n",
+ "[177] 210.000 800.000 240.000 350.000 175.000 200.000 1940.000 700.000\n",
+ "[185] 750.000 450.000 172.000 1260.000 750.000 190.000 580.000 130.000\n",
+ "[193] 450.000 300.000 250.000 1050.000 215.000 400.000 560.000 1670.000\n",
+ "[201] 487.500 425.000 500.000 250.000 400.000 450.000 750.000 70.000\n",
+ "[209] 875.000 190.000 191.000 740.000 250.000 140.000 97.500 740.000\n",
+ "[217] 140.000 341.667 1000.000 100.000 90.000 200.000 135.000 155.000\n",
+ "[225] 475.000 1450.000 150.000 105.000 350.000 90.000 530.000 341.667\n",
+ "[233] 940.000 350.000 326.667 250.000 740.000 425.000 925.000 185.000\n",
+ "[241] 920.000 286.667 245.000 235.000 1150.000 160.000 425.000 900.000\n",
+ "[249] 500.000 277.500 750.000 160.000 1300.000 525.000 550.000 1600.000\n",
+ "[257] 120.000 165.000 700.000 875.000 385.000 960.000 1000.000"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
- "sum(is.na(Hitters$Salary))"
+ "Hitters$Salary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hence we see that Salary is missing for 59 players. The `na.omit()` function\n",
"removes all of the rows that have missing values in any variable."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 111,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:15:19.053026Z",
"start_time": "2019-10-14T16:15:19.035Z"
}
},
"outputs": [],
"source": [
"Hitters = na.omit(Hitters)"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:15:38.210475Z",
"start_time": "2019-10-14T16:15:38.187Z"
}
},
"source": [
"Write in the following the code to perform best subset selection with up to 19 predictors and plot the adjusted R^2 against the number of predictors.\n",
"\n",
"Hint: What argument do you need to set in `regsubsets()` to do best subset selection?"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 112,
"metadata": {},
"outputs": [],
- "source": []
+ "source": [
+ "regfit.best = regsubsets(Salary ~ ., data = Hitters, method = \"exhaustive\", nvmax = 19)\n",
+ "regfit.best.summary = summary(regfit.best)"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Determine the optimal number of predictors according to the adjusted R^2 criterion and the BIC criterion."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 113,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1] 6\n",
+ "[1] 11\n"
+ ]
+ }
+ ],
+ "source": [
+ "bic.min = which.min(regfit.best.summary$bic)\n",
+ "print(bic.min)\n",
+ "adjr2.max = which.max(regfit.best.summary$adjr2)\n",
+ "print(adjr2.max)"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Write in the following the code to perform best subset selection with 10-fold cross-validation (the right way).\n",
"\n",
"Once you have written the code, you can run the same cell multiple times to get the results for different random seeds."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 141,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1] 10\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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YqdgnDHDgAAlIab3AGKyZR97VzSqfMp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\n",
+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "k = 10\n",
+ "folds = sample(1:k, nrow(Hitters), replace = T)\n",
+ "cv.errors = matrix(NA, k, 19)\n",
+ "for (j in 1:k) {\n",
+ " regfit.best = regsubsets(Salary ~ ., data = Hitters[folds!=j,], method = \"exhaustive\", nvmax = 19)\n",
+ " for (i in 1:19) {\n",
+ " pred = predict(regfit.best, Hitters[folds==j,], id = i)\n",
+ " cv.errors[j,i] = mean( (Hitters$Salary[folds==j] - pred)^2 )\n",
+ " }\n",
+ "}\n",
+ "mean.cv.errors = apply(cv.errors, 2, mean)\n",
+ "plot(mean.cv.errors, type = \"l\",\n",
+ " xlab = \"Number of Variables\", ylab = \"10-fold CV right\")\n",
+ "cv.min = which.min(mean.cv.errors)\n",
+ "print(cv.min)\n",
+ "points(cv.min, mean.cv.errors[cv.min], col = \"red\", cex = 2, pch = 20)"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once you are convinced about the right number of variables, you can perform best subset selection on the full data set to obtain the best fit for the parameters of that model. To do so, assign your choice of the number of parameters to `i_best` and run the cell."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"i_best = \n",
"reg.best = regsubsets(Salary ~ ., data = Hitters, nvmax = 19)\n",
"coef(reg.best, i_best)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now you are ready to do the following quiz. If you see `You do not have access to this content. Try logging in.` you have to log into your moodle account in a separate browser window and then return to this page."
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T19:27:31.332705Z",
"start_time": "2019-10-14T19:27:31.315Z"
},
"hide_input": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"IRdisplay::display_html('')"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": true
},
"source": [
"## Validation Set Approach (optional)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now perform best subset selection with the validation set approach. For this, we split the data first into training and validation set.\n",
"Then, we apply `regsubsets()` to the training set in order to perform best\n",
"subset selection."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:34:42.188507Z",
"start_time": "2019-10-14T16:34:42.162Z"
}
},
"outputs": [],
"source": [
"set.seed(1)\n",
"train = sample(c(TRUE,FALSE), nrow(Hitters), rep = TRUE)\n",
"test = (!train)\n",
"regfit.best = regsubsets(Salary ~ ., data = Hitters[train,], nvmax = 19)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:34:47.159461Z",
"start_time": "2019-10-14T16:34:47.142Z"
}
},
"outputs": [],
"source": [
"test.mat = model.matrix(Salary ~ ., data = Hitters[test,])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model.matrix() function is used in many regression packages for building an “X” matrix from data. Now we run a loop, and for each size i, we extract the coefficients from `regfit.best` for the best model of that size,\n",
"multiply them into the appropriate columns of the test model matrix to\n",
"form the predictions, and compute the test MSE. The symbol `%*%` stands for matrix multiplication."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:39:19.843578Z",
"start_time": "2019-10-14T16:39:19.790Z"
}
},
"outputs": [],
"source": [
"val.errors = rep(NA ,19)\n",
"for ( i in 1:19) {\n",
" coefi = coef(regfit.best, id = i)\n",
" pred = test.mat[, names(coefi)] %*% coefi\n",
" val.errors[i] = mean((Hitters$Salary[test] - pred)^2)\n",
"}\n",
"val.errors"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-14T16:39:34.117682Z",
"start_time": "2019-10-14T16:39:34.098Z"
}
},
"outputs": [],
"source": [
"which.min(val.errors)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false
},
"source": [
"This was a little tedious, partly because there is no `predict()` method\n",
"for `regsubsets()`. This is why we wrote the function `predict.regsubsets` above. Our function pretty much mimics what we did above. The only complex part is how we extracted the formula used in the call to `regsubsets()`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/src/polynomials_and_splines.ipynb b/src/polynomials_and_splines.ipynb
index fede905..769a34b 100644
--- a/src/polynomials_and_splines.ipynb
+++ b/src/polynomials_and_splines.ipynb
@@ -1,980 +1,992 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Polynomials and Splines"
]
},
{
"cell_type": "code",
"execution_count": 191,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"IRdisplay::display_html('')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"New R commands:\n",
"* `poly(predictor, order, raw = FALSE)`\n",
"* `I()`\n",
"* `cbind()`\n",
"* `cut(predictor, number_of_cuts)`\n",
"* `bs(predictor, degree = 3, knots = , df = )`\n",
"* `ns(predictor, degree = 3, knots = , df = )`\n",
"* `smooth.spline(predictor, response)`\n",
"\n",
"Useful R commands to remember:\n",
"* `range(column)` gives lower and upper bounds for the data in `column`.\n",
" \n",
"\n",
"This section is inspired by the Lab in chapter 7 from the textbook.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Regression"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"library(ISLR)\n",
"attach(Wage)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will look at the Wage data, which contains the following columns."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"names(Wage)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us have a look at the first five rows of columns age (the second column) and wage (the 11th column).\n",
"We see that the first individual has age 18 and a wage of 75'000 US Dollar per year."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Wage[1:5,c(2, 11)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To use multiple powers of `age` as predictors, we can use the `poly` function. With the argument `raw = T` (short form of `raw = TRUE`), we see that it effectively computes higher powers of `age`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"poly(Wage$age[1:5], 4, raw = T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By default, `raw = F`, in which case the `poly` function returns an orthogonal basis formed by linear combination of all powers of `age`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"poly(Wage$age[1:5], 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now see that the estimate of the coefficients depends on whether we choose the orthogonal or the raw basis, but the predictions do not depend on this choice."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit1 = lm(wage ~ poly(age, 4), data = Wage)\n",
"coef(summary(fit1))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit2 = lm(wage ~ poly(age, 4, raw = TRUE), data = Wage)\n",
"coef(summary(fit2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remember that the `predict` function without any further arguments computes the prediction of the model on the training set.\n",
"We see here that the prediction for the first individual is approximately 52'000 USD. Remember that the first individiual is 18 years old and has an actual wage of 75'000 USD. There are probably other individuals of 18 years of age in the training set with a much lower income."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"predict(fit1)[1:5]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"predict(fit2)[1:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As an alternative to the `poly` function we could have explicitly defined our predictors using the wrappers `I` (the \"as-is\" operator) or `cbind`. These wrappers are needed because `^` has a special meaning in formulas.\n",
"The `cbind` function builds a matrix from a collection of vectors.\n",
"\n",
"Both variants create a predictors of the same form as `poly(age, 4, raw = T)`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit3 = lm(wage ~ I(age) + I(age^2) + I(age^3) + I(age^4), data = Wage)\n",
"predict(fit3)[1:5]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit4 = lm(wage ~ cbind(age, age^2, age^3, age^4), data = Wage)\n",
"predict(fit4)[1:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now create a grid of values for `age` at which predictions. We first extract the lower and upper bound of the values in the `age` column."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"agelims = range(age)\n",
"agelims"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then create a grid of 50 points between these bounds."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"age.grid = seq(from = agelims[1], to = agelims[2], length = 50)\n",
"age.grid"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And then call the generic `predict()` function, specifying that we want standard errors as well."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"predictions = predict(fit1, newdata = list(age = age.grid), se = T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The prediction of the standard errors is stored in the column `se.fit`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"names(predictions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create now a matrix that contains the predictions plus/minus two times the standard deviation, which corresponds to an approximate 95% confidence interval for normally distributed errors."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"se.bands = cbind(predictions$fit - 2 * predictions$se.fit, predictions$fit + 2 * predictions$se.fit)\n",
"se.bands[1:5,]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will plot now the data together with the predictions. Use `?par` or `?plot` to get help on arguments that you don't understand."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(age, wage, xlim = agelims, cex = .5, col = \"darkgrey\")\n",
"title(\"Degree-4 Polynomial\")\n",
"lines(age.grid, predictions$fit, lwd = 2, col = \"blue\")\n",
"matlines(age.grid, se.bands, lwd = 1, col = \"blue\", lty = 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to fit a step function we use the `cut()` function. We use the function `table()` to display what `cut()` does."
]
},
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# NOTE: cut can run into issues:\n",
+ "k = sample(1:10, length(wage), replace = T)\n",
+ "fit = lm(wage ~ cut(age, 4, include.lowest = T), data = Wage[k != 2,])\n",
+ "predict(fit, Wage[k == 2,])"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"table(cut(age, 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, `cut()` automatically picked the cutpoints at 33.5, 49 and 64.5 years of age.\n",
"The lower row displays the number of data points that fall into each region.\n",
"\n",
"The function `cut()` returns an ordered categorical variable; the `lm()` function then creates a set of dummy variables for use in the regression. The `age < 33.5` category is left out, so the intercept coefficient of 94'160 USD can be interpreted as the average salary for those under 33.5 years of age, and the other coefficients can be interpreted as the average additional salary for those in the other age groups."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit.steps = lm(wage ~ cut(age, 4), data = Wage)\n",
"coef(summary(fit.steps))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Classification"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we consider the task of predicting whether an individual earns more than 250'000 USD per year."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit = glm(I(wage > 250) ~ poly(age, 4), data = Wage, family = binomial)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that we again use the wrapper `I()` to create this binary response variable on the fly. The expression `wage>250` evaluates to a logical variable containing `TRUE`s and `FALSE`s, which `glm()` coerces to binary by setting the `TRUE`s to 1 and the `FALSE`s to 0.\n",
"\n",
"Once again, we make predictions using the `predict()` function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"preds = predict(fit, newdata = list(age = age.grid), se = T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, calculating the confidence intervals is slightly more involved than in the linear regression case.\n",
"The default prediction type for a `glm()` model is `type = \"link\"`, which is what we use here. This means we get predictions for the logit."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"se.bands.logit = cbind(preds$fit - 2*preds$se.fit, preds$fit + 2*preds$se.fit)\n",
"se.bands.logit[1:5,]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To transform them to probabilities we use the formula $p(Y=1|X) = \\frac{\\exp(\\beta X)}{1 + \\exp(\\beta X)}$, where $\\beta X = \\beta_0 + \\beta_1 X + \\beta_2 X^2 + \\beta_3X^3 + \\beta_4X^4$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"se.bands = exp(se.bands.logit)/(1 + exp(se.bands.logit))\n",
"cbind(age.grid[1:5], se.bands[1:5,])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the predicted confidence interval for the probabilities to earn more than 250'000USD per year is rather narrow and at low probabilities for ages up to 23 years.\n",
"\n",
"Now we will plot again. The `jitter` function is used to jitter the `age` values a bit so that observations with the same `age` value do not cover each other up. This is often called a rug plot."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(age, I(wage>250), xlim = agelims, type = \"n\", col = \"darkgrey\", ylim = c(0, .2))\n",
"points(jitter(age), I((wage>250)*.2), cex = .5, pch = \"|\", col = \"darkgrey\") # since we plot only up to 0.2 we plot the TRUEs at 0.2\n",
"title(\"Degree-4 Polynomial\")\n",
"lines(age.grid, exp(preds$fit)/(1 + exp(preds$fit)), lwd = 2, col = \"blue\")\n",
"matlines(age.grid, se.bands, lwd = 1, col = \"blue\", lty = 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Splines"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the `splines` library.\n",
"\n",
"In the lecture we saw that regression splines can be fit by constructing an appropriate matrix of basis functions. The `bs()` function generates the entire matrix of basis functions for splines with the specified set of knots. By default, cubic splines are produced."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"library(splines)\n",
"spline.fit = lm(wage ~ bs(age, knots = c(25, 40, 60)), data = Wage)\n",
"spline.pred = predict(spline.fit, newdata = list(age = age.grid), se = T)\n",
"plot(age, wage, col = \"gray\")\n",
"lines(age.grid, spline.pred$fit, lwd = 2)\n",
"lines(age.grid, spline.pred$fit - 2*spline.pred$se.fit, lty = \"dashed\")\n",
"lines(age.grid, spline.pred$fit + 2*spline.pred$se.fit, lty = \"dashed\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Above we have prespecified knots at ages 25, 40 and 60. This produces a spline with six basis functions.\n",
"Recall that a cubic spline with three knots has seven degrees of freedom; these degrees of freedom are used up by an intercept, plus six basis functions. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"dim(bs(age, knots = c(25, 40, 60)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could also use the `df` option to produce a spline with knots at uniform quantiles of the data."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"dim(bs(age, df = 6))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case `R` chooses knots at ages 33.8, 42 and 51, which corresponds to the 25th, 50th and 75th percentiles of age."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"attr(bs(age, df = 6), \"knots\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function `bs()` also has a `degree` argument, so we can fit splines of any degree, rather than the default degree of 3 (which yields a cubic spline)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"dim(bs(age, knots = c(25, 40, 60), degree = 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to instead fit a natural spline, we use the `ns()` function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"ns.fit = lm(wage ~ ns(age, knots = c(25, 40, 60), Boundary.knots = c(0, 100)), data = Wage)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To compare the different methods in how they interpolate and extrapolate we use now a larger range and plot the predictions of the different methods."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"age.grid = seq(0, 100, length = 100)\n",
"ns.pred = predict(ns.fit, newdata = list(age = age.grid), se = T)\n",
"bs.pred = predict(lm(wage ~ bs(age, knots = c(25, 40, 60), Boundary.knots = c(0, 100)), data = Wage), newdata = list(age = age.grid), se = T)\n",
"p4.pred = predict(lm(wage ~ poly(age, 4), data = Wage), newdata = list(age = age.grid), se = T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make the plotting a bit more convenient we use the following function"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot.predictions = function(ages, pred, col = \"blue\") {\n",
" se.bands = cbind(pred$fit - 2 * pred$se.fit, pred$fit + 2 * pred$se.fit)\n",
" lines(ages, pred$fit, lwd = 2, col = col)\n",
" matlines(ages, se.bands, lty = \"dashed\", col = col)\n",
"}\n",
"plot(age, wage, cex = .5, col = \"darkgrey\", xlim = c(0, 100), ylim = c(-20, 300))\n",
"plot.predictions(age.grid, ns.pred, col = \"red\")\n",
"plot.predictions(age.grid, bs.pred, col = \"darkgreen\")\n",
"plot.predictions(age.grid, p4.pred, col = \"blue\")\n",
"legend(x = 25, y = 20, legend = c(\"natural cubic spline\", \"cubic spline\", \"4th order polynomial\"),\n",
" col = c(\"red\", \"darkgreen\", \"blue\"), lty = 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Smoothing Splines"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to fit a smoothing spline, we use the `smooth.spline()` function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit.smooth.cv = smooth.spline(age, wage)\n",
"fit.smooth.cv"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see the selected Degrees of Freedom using cross-validation.\n",
"If instead we wish to set the defgrees of freedom manually, we can use"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fit.smooth = smooth.spline(age, wage, df = 16)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let us plot the two smoothing splines."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(age, wage, cex = .5, col = \"darkgrey\", xlim = agelims)\n",
"lines(fit.smooth, col = \"red\", lwd = 2)\n",
"lines(fit.smooth.cv, col = \"blue\", lwd = 2)\n",
"legend(\"topright\", legend = c(\"16 Df\", \"6.5 DF\"), col = c(\"red\", \"blue\"), lty - 1, lwd = 2, cex = .8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## GAMs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now fit a GAM to predict `wage` using natural spline functions of `year` and `age`, treating `education` as a qualitative predictor. Since this is just a big linear regressions model using an appropriate choice of basis functions, we can simply do this using the `lm()` function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"gam1 = lm(wage ~ ns(year, 4) + ns(age, 5) + education, data = Wage)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot predictions of `wage` given `age` while fixing the other variables to e.g. `year = 2005` and `education = \"1. < HS Grad\"`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"pred.1 = predict(gam1, newdata = data.frame(age = age.grid,\n",
" year = rep(2005, length(age.grid)),\n",
" education = rep(\"1. < HS Grad\", length(age.grid))))\n",
"pred.2 = predict(gam1, newdata = data.frame(age = age.grid,\n",
" year = rep(2005, length(age.grid)),\n",
" education = rep(\"4. College Grad\", length(age.grid))))\n",
"pred.3 = predict(gam1, newdata = data.frame(age = age.grid,\n",
" year = rep(2009, length(age.grid)),\n",
" education = rep(\"1. < HS Grad\", length(age.grid))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For plotting we select now all data in the years 2004 to 2006 for individuals with less than a High School degree and plot it together with our prediction."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"subset = year >= 2004 & year <= 2006 & education == \"1. < HS Grad\"\n",
"plot(age[subset], wage[subset])\n",
"lines(age.grid, pred.1, type = \"l\", col = \"red\")\n",
"lines(age.grid, pred.2, type = \"l\", col = \"blue\")\n",
"lines(age.grid, pred.3, type = \"l\", col = \"darkgreen\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the prediction for individual with a College Graduation or the prediction for the year 2009 is merely a shifted version of the original prediction. This is a consequence of the additivity of the model. The shape of the function `wage = f(age)` is independent of the other predictors; only the absolute level is influenced by the intercept and the other predictors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For smoothing splines we use the `gam` library. The `s()` function is used to indicate that we would like to use a smoothing spline.\n",
" \n",
"The `gam` library also has a built-in plotting function that allows us to see the dependence of the `wage` independently of the other variables. Note that we would have to add the intercept and the choices for the other predictors to get the effective prediction of wage."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"library(gam)\n",
"gam.m3 = gam(wage ~ s(year, 4) + s(age, 5) + education, data = Wage)\n",
"plot(gam.m3, se = T, col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bias-Variance Decomposition (optional)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the first lecture we saw the decomposition of the test error into bias and variance as a function of the flexibility of the method. With smoothing splines one can nicely generate such plots.\n",
"\n",
"The following code is at parts more involved than what you are used to. Try nevertheless to understand what is happing. You are not yet expected to write such code without guidance.\n",
"\n",
"The idea is to generate artificial data, where we know exactly what the true model is. The true model is given by the non-linear function `noisefree.generator`. The function `data.generator` creates each time a new data set by sampling some `x` values, applying the `noisefree.generator` function and adding normal noise with standard deviation 1 to get `y`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"noisefree.generator = function(x) (-.1*(x-1)^4*(x < 1) - 2*x^3*sin(5*x) + x^2 - 4*x*(x > 0))\n",
"data.generator = function(n) {\n",
" x = 3*runif(n) - 1.5\n",
" y = noisefree.generator(x) + rnorm(length(x))\n",
" data.frame(x = x, y = y)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us plot some data points and some smooth spline fits together with the true function in red."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data = data.generator(200)\n",
"fit.1 = smooth.spline(data$x, data$y, df = 2)\n",
"fit.2 = smooth.spline(data$x, data$y, df = 20)\n",
"fit.3 = smooth.spline(data$x, data$y, df = 100)\n",
"plot(data, col = \"darkgray\")\n",
"lines(fit.1, col = \"purple\")\n",
"lines(fit.2, col = \"darkgreen\")\n",
"lines(fit.3, col = \"blue\")\n",
"plot(noisefree.generator, add = T, xlim = c(-1.5, 1.5), col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we create to functions that compute test and training errors for a given fit. The test error will be evaluated over 10000 new data points."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"test.error = function(fit) {\n",
" test.data = data.generator(10000)\n",
" pred = predict(fit, test.data$x)\n",
" mean((pred$y - test.data$y)^2)\n",
"}\n",
"train.error = function(fit, x, y) {\n",
" mean((predict(fit, x)$y - y)^2)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list(test.error(fit.1), test.error(fit.2), test.error(fit.3))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list(train.error(fit.1, data$x, data$y), train.error(fit.2, data$x, data$y), train.error(fit.3, data$x, data$y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following function `bias.variance` takes as input the number `k` of repetitions and the degree of freedom `df`. It then fits `k` times a smoothing spline of degree `df` on `k` different training sets from the same population.\n",
"\n",
"The squared bias of the model is then the mean squared difference between the average of the `k` smoothing splines and the true function.\n",
"\n",
"The variance is simply the variance of the `k` smoothing splines.\n",
"\n",
"Additionally we return the average test and training error."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"bias.variance = function(k, df = df) {\n",
" predictions = matrix(rep(NA, k*1000), k, 1000)\n",
" train.errors = rep(NA, k)\n",
" test.errors = rep(NA, k)\n",
" test.x = seq(-1.5, 1.5, length = 1000)\n",
" for (i in 1:k) {\n",
" data = data.generator(200) # each time another training set\n",
" fit = smooth.spline(data$x, data$y, df = df)\n",
" train.errors[i] = train.error(fit, data$x, data$y)\n",
" test.errors[i] = test.error(fit)\n",
" predictions[i,] = predict(fit, test.x)$y # function values for this fit\n",
" }\n",
" mean.pred = apply(predictions, 2, mean)\n",
" bias.squared = mean((mean.pred - noisefree.generator(test.x))^2)\n",
" var = mean(sweep(predictions, 2, mean.pred)^2)\n",
" data.frame(bias.squared = bias.squared,\n",
" variance = var, \n",
" test.error = mean(test.errors), \n",
" train.error = mean(train.errors))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we run this function for many different degrees of freedom and plot the result. Evaluating this cell takes some minutes. You can also just look at the output from a previous run. We marked the irreducible error with a dashed line."
]
},
{
"cell_type": "code",
"execution_count": 185,
"metadata": {},
"outputs": [
{
"data": {
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EaRJPfJAgAAZAJhpwKzGTu9XiKEGTsA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OblKHJbJ3LHa2TBCE7OxsqVMQkZyYWk2WAnek+qMYOXoAACAASURBVEhedV5udW5j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\ngg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"biases = rep(NA, 50)\n",
"variances = rep(NA, 50)\n",
"trainerr = rep(NA, 50)\n",
"testerr = rep(NA, 50)\n",
"for (i in 1:50) {\n",
" res = bias.variance(1000, 2*i)\n",
" biases[i] = res$bias.squared\n",
" variances[i] = res$variance\n",
" trainerr[i] = res$train.error\n",
" testerr[i] = res$test.error\n",
"}\n",
"df = 2*(1:50)\n",
"plot(df, biases, col = \"black\", type = \"l\", ylim = c(0, 4), xlab = \"DF\", ylab = \"error\")\n",
"lines(df, variances, col = \"darkgreen\")\n",
"lines(df, trainerr, col = \"blue\")\n",
"lines(df, testerr, col = \"red\")\n",
"lines(df, rep(1, 50), lty = \"dashed\")\n",
"legend(\"topright\", legend = c(\"bias^2\", \"variance\", \"training error\", \"test error\"),\n",
" col = c(\"black\", \"darkgreen\", \"blue\", \"red\"), lty = 1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
- "version": "3.6.1"
+ "version": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/src/ridge_regression_and_lasso.ipynb b/src/ridge_regression_and_lasso.ipynb
index 35885e6..805bc65 100644
--- a/src/ridge_regression_and_lasso.ipynb
+++ b/src/ridge_regression_and_lasso.ipynb
@@ -1,442 +1,1241 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Ridge Regression and the Lasso"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"New R commands:\n",
"* `glmnet(x, y, alpha = , lambda = )`\n",
"* `model.matrix(formula, data)`\n",
"\n",
"Useful R commands to remember:\n",
"* `seq(from, to, length = )` create a list of a given `length` of linearly spaced numbers between `from` and `to`.\n",
" \n",
"\n",
"This section follows the Lab 2 in chapter 6 from the textbook.\n",
"\n",
"We will use the `glmnet` package in order to perform ridge regression and\n",
"the lasso. The main function in this package is `glmnet()`, which can be used\n",
"to fit ridge regression models, lasso models, and more. This function has\n",
"slightly different syntax from other model-fitting functions that we have\n",
"encountered thus far in this book. In particular, we must pass in an x\n",
"matrix as well as a y vector, and we do not use the y ∼ x syntax. We will\n",
"now perform ridge regression and the lasso in order to predict Salary on\n",
"the Hitters data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ridge regression"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 99,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\t- 'AtBat'
\n",
+ "\t- 'Hits'
\n",
+ "\t- 'HmRun'
\n",
+ "\t- 'Runs'
\n",
+ "\t- 'RBI'
\n",
+ "\t- 'Walks'
\n",
+ "\t- 'Years'
\n",
+ "\t- 'CAtBat'
\n",
+ "\t- 'CHits'
\n",
+ "\t- 'CHmRun'
\n",
+ "\t- 'CRuns'
\n",
+ "\t- 'CRBI'
\n",
+ "\t- 'CWalks'
\n",
+ "\t- 'League'
\n",
+ "\t- 'Division'
\n",
+ "\t- 'PutOuts'
\n",
+ "\t- 'Assists'
\n",
+ "\t- 'Errors'
\n",
+ "\t- 'Salary'
\n",
+ "\t- 'NewLeague'
\n",
+ "
\n"
+ ],
+ "text/latex": [
+ "\\begin{enumerate*}\n",
+ "\\item 'AtBat'\n",
+ "\\item 'Hits'\n",
+ "\\item 'HmRun'\n",
+ "\\item 'Runs'\n",
+ "\\item 'RBI'\n",
+ "\\item 'Walks'\n",
+ "\\item 'Years'\n",
+ "\\item 'CAtBat'\n",
+ "\\item 'CHits'\n",
+ "\\item 'CHmRun'\n",
+ "\\item 'CRuns'\n",
+ "\\item 'CRBI'\n",
+ "\\item 'CWalks'\n",
+ "\\item 'League'\n",
+ "\\item 'Division'\n",
+ "\\item 'PutOuts'\n",
+ "\\item 'Assists'\n",
+ "\\item 'Errors'\n",
+ "\\item 'Salary'\n",
+ "\\item 'NewLeague'\n",
+ "\\end{enumerate*}\n"
+ ],
+ "text/markdown": [
+ "1. 'AtBat'\n",
+ "2. 'Hits'\n",
+ "3. 'HmRun'\n",
+ "4. 'Runs'\n",
+ "5. 'RBI'\n",
+ "6. 'Walks'\n",
+ "7. 'Years'\n",
+ "8. 'CAtBat'\n",
+ "9. 'CHits'\n",
+ "10. 'CHmRun'\n",
+ "11. 'CRuns'\n",
+ "12. 'CRBI'\n",
+ "13. 'CWalks'\n",
+ "14. 'League'\n",
+ "15. 'Division'\n",
+ "16. 'PutOuts'\n",
+ "17. 'Assists'\n",
+ "18. 'Errors'\n",
+ "19. 'Salary'\n",
+ "20. 'NewLeague'\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ " [1] \"AtBat\" \"Hits\" \"HmRun\" \"Runs\" \"RBI\" \"Walks\" \n",
+ " [7] \"Years\" \"CAtBat\" \"CHits\" \"CHmRun\" \"CRuns\" \"CRBI\" \n",
+ "[13] \"CWalks\" \"League\" \"Division\" \"PutOuts\" \"Assists\" \"Errors\" \n",
+ "[19] \"Salary\" \"NewLeague\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"library(ISLR)\n",
"names(Hitters)\n",
"Hitters = na.omit(Hitters)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `model.matrix()` function is particularly useful for creating x; not only\n",
"does it produce a matrix corresponding to the 19 predictors but it also\n",
"automatically transforms any qualitative variables into dummy variables.\n",
"The latter property is important because `glmnet()` can only take numerical,\n",
"quantitative inputs. We remove the first column returned by `model.matrix()`,\n",
"since it only contains ones that are only needed when fitting an intercept with other methods. "
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 100,
"metadata": {},
"outputs": [],
"source": [
"x = model.matrix(Salary~., Hitters)[,-1]\n",
"y = Hitters$Salary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `glmnet()` function has an `alpha` argument that determines what type\n",
"of model is fit. If `alpha=0` then a ridge regression model is fit, and if `alpha=1`\n",
"then a lasso model is fit. We first fit a ridge regression model."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 101,
"metadata": {},
"outputs": [],
"source": [
"library(glmnet)\n",
"grid = 10^seq(10, -2, length = 100)\n",
"ridge.mod = glmnet(x, y, alpha = 0, lambda = grid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By default the `glmnet()` function performs ridge regression for an automatically selected range of λ values. However, here we have chosen to implement\n",
"the function over a grid of values ranging from $\\lambda = 10^{10}$ to $\\lambda = 10^{-2}$.\n",
"Note that by default, the `glmnet()` function standardizes the\n",
"variables so that they are on the same scale. To turn off this default setting,\n",
"use the argument `standardize=FALSE`.\n",
"\n",
"Associated with each value of λ is a vector of ridge regression coefficients,\n",
"stored in a matrix that can be accessed by `coef()`. In this case, it is a 20×100\n",
"matrix, with 20 rows (one for each predictor, plus an intercept) and 100\n",
"columns (one for each value of λ).\n",
"We expect the coefficient estimates to be much smaller, in terms of $\\ell_2$ norm,\n",
"when a large value of λ is used, as compared to when a small value of λ is\n",
"used. \n",
"\n",
"Check that this is the case by repeating the following steps for another index than 50."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 102,
"metadata": {},
- "outputs": [],
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"source": [
"ridge.mod$lambda[50]"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 103,
"metadata": {},
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"source": [
"coef(ridge.mod)[,50]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we exclude the intercept and compute the $\\ell_2$ norm of the coefficients."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 104,
"metadata": {},
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"source": [
"sqrt(sum(coef(ridge.mod)[-1,50]^2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use the `predict()` function for a number of purposes. For instance,\n",
"we can obtain the ridge regression coefficients for a new value of λ, say 50:"
]
},
{
"cell_type": "code",
- "execution_count": null,
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"metadata": {},
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+ " (Intercept) AtBat Hits HmRun Runs \n",
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"source": [
"predict(ridge.mod, s = 50, type = \"coefficients\")[1:20,]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now split the samples into a training set and a test set in order\n",
"to estimate the test error of ridge regression and the lasso.\n",
"There are two\n",
"common ways to randomly split a data set. The first is to produce a random\n",
"vector of TRUE, FALSE elements and select the observations corresponding to\n",
"TRUE for the training data. The second is to randomly choose a subset of\n",
"numbers between 1 and n; these can then be used as the indices for the\n",
"training observations. The two approaches work equally well."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"set.seed(1)\n",
"train = sample(1:nrow(x), nrow(x)/2)\n",
"test = (-train)\n",
"y.test = y[test]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we fit a ridge regression model on the training set, and evaluate\n",
"its MSE on the test set, using λ = 4. Note the use of the `predict()`\n",
"function again. This time we get predictions for a test set, by replacing\n",
"`type=\"coefficients\"` with the `newx` argument."
]
},
{
"cell_type": "code",
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- "outputs": [],
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+ "text/html": [
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+ "[1] 142226.5"
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"source": [
"ridge.mod = glmnet(x[train,], y[train], alpha = 0, lambda = grid)\n",
"ridge.pred = predict(ridge.mod, s = 4, newx = x[test,])\n",
"mean((ridge.pred - y.test)^2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remember that in the extreme case of λ approaching infinite, all coefficients are shrunk to zero,\n",
"which corresponds to fitting a model with only an intercept.\n",
"Let us check that this is the case for our fit."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 108,
"metadata": {},
- "outputs": [],
+ "outputs": [
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+ "text/html": [
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+ "metadata": {},
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"source": [
"ridge.pred = predict(ridge.mod, s = 10^200, newx = x[test,])\n",
"mean((ridge.pred - y.test)^2)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 109,
"metadata": {},
- "outputs": [],
+ "outputs": [
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+ "data": {
+ "text/html": [
+ "224669.906736192"
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+ "224669.906736192"
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"source": [
"mean((mean(y[train]) - y.test)^2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So fitting a ridge regression model with λ = 4 leads to a much lower test\n",
"MSE than fitting a model with just an intercept.\n",
"\n",
"We now check whether\n",
"there is any benefit to performing ridge regression with λ = 4 instead of\n",
"just performing least squares regression. Recall that least squares is simply\n",
"ridge regression with λ = 0. While the two methods yield very similar results,\n",
"it is unclear to me why there are still small differences."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 110,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "167018.249850993"
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"source": [
"ridge.pred = predict(ridge.mod, s=0, newx=x[test,], exact=T, x=x[train,], y=y[train])\n",
"mean((ridge.pred-y.test)^2)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 111,
"metadata": {},
- "outputs": [],
+ "outputs": [
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+ "text/html": [
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"source": [
"lm.pred = predict(lm(Salary ~ ., data = Hitters, subset=train), Hitters[test,])\n",
"mean((lm.pred-y.test)^2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In general, instead of arbitrarily choosing λ = 4, it would be better to\n",
"use cross-validation to choose the tuning parameter λ. We can do this using\n",
"the built-in cross-validation function, `cv.glmnet()`. By default, the function\n",
"performs ten-fold cross-validation, though this can be changed using the\n",
"argument `nfolds`. Note that we set a random seed first so our results will\n",
"be reproducible, since the choice of the cross-validation folds is random."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 112,
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M4FLsVGxMZ60sq1K1JendtJfdOjzGd+/yOTPCfFNGfYGsDdQ3gCmHG58MSNGzcE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yvu/ZV+uzbO+7u35jNqw/s6BRewrGElIU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\nWlJS0rhiMBiI6Ny5c9zDGIaJjIz09va+lyFBBFCeAJAOBDu4KTo62mLl6tW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5fI8nGLgUCzd5hA6IjfVui5u3bIeq6+Rdpwf+tOLr7YkX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\nAIjE/wetrgqQ1rsvqwAAAABJRU5ErkJggg==",
+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
"source": [
"set.seed(1)\n",
"cv.out=cv.glmnet(x[train,],y[train],alpha=0)\n",
"plot(cv.out)\n",
"bestlam=cv.out$lambda.min\n",
"bestlam"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Take the best lambda `bestlam` and compute the mean squared error on the test set.\n",
"\n",
"Is there a further improvement in test error over the arbitrary choice of λ = 4?"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 115,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "139833.615684819"
+ ],
+ "text/latex": [
+ "139833.615684819"
+ ],
+ "text/markdown": [
+ "139833.615684819"
+ ],
+ "text/plain": [
+ "[1] 139833.6"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ridge.pred.best = predict(ridge.mod, s=bestlam, newx=x[test,])\n",
+ "mean((ridge.pred.best-y.test)^2)"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we refit our ridge regression model on the full data set,\n",
"using the value of λ chosen by cross-validation, and examine the coefficient\n",
"estimates."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 116,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\t- (Intercept)
\n",
+ "\t\t- 15.4438313539103
\n",
+ "\t- AtBat
\n",
+ "\t\t- 0.0771554748907925
\n",
+ "\t- Hits
\n",
+ "\t\t- 0.859115814031969
\n",
+ "\t- HmRun
\n",
+ "\t\t- 0.601031069746882
\n",
+ "\t- Runs
\n",
+ "\t\t- 1.06369006654778
\n",
+ "\t- RBI
\n",
+ "\t\t- 0.879361053365972
\n",
+ "\t- Walks
\n",
+ "\t\t- 1.62444616279791
\n",
+ "\t- Years
\n",
+ "\t\t- 1.35254779528422
\n",
+ "\t- CAtBat
\n",
+ "\t\t- 0.0113499915102498
\n",
+ "\t- CHits
\n",
+ "\t\t- 0.0574665439614789
\n",
+ "\t- CHmRun
\n",
+ "\t\t- 0.406801566464205
\n",
+ "\t- CRuns
\n",
+ "\t\t- 0.114562244309134
\n",
+ "\t- CRBI
\n",
+ "\t\t- 0.121165037864304
\n",
+ "\t- CWalks
\n",
+ "\t\t- 0.0529920199108252
\n",
+ "\t- LeagueN
\n",
+ "\t\t- 22.0914318947081
\n",
+ "\t- DivisionW
\n",
+ "\t\t- -79.0403263679412
\n",
+ "\t- PutOuts
\n",
+ "\t\t- 0.166199027482507
\n",
+ "\t- Assists
\n",
+ "\t\t- 0.0294194957326422
\n",
+ "\t- Errors
\n",
+ "\t\t- -1.36092944882302
\n",
+ "\t- NewLeagueN
\n",
+ "\t\t- 9.12487766980244
\n",
+ "
\n"
+ ],
+ "text/latex": [
+ "\\begin{description*}\n",
+ "\\item[(Intercept)] 15.4438313539103\n",
+ "\\item[AtBat] 0.0771554748907925\n",
+ "\\item[Hits] 0.859115814031969\n",
+ "\\item[HmRun] 0.601031069746882\n",
+ "\\item[Runs] 1.06369006654778\n",
+ "\\item[RBI] 0.879361053365972\n",
+ "\\item[Walks] 1.62444616279791\n",
+ "\\item[Years] 1.35254779528422\n",
+ "\\item[CAtBat] 0.0113499915102498\n",
+ "\\item[CHits] 0.0574665439614789\n",
+ "\\item[CHmRun] 0.406801566464205\n",
+ "\\item[CRuns] 0.114562244309134\n",
+ "\\item[CRBI] 0.121165037864304\n",
+ "\\item[CWalks] 0.0529920199108252\n",
+ "\\item[LeagueN] 22.0914318947081\n",
+ "\\item[DivisionW] -79.0403263679412\n",
+ "\\item[PutOuts] 0.166199027482507\n",
+ "\\item[Assists] 0.0294194957326422\n",
+ "\\item[Errors] -1.36092944882302\n",
+ "\\item[NewLeagueN] 9.12487766980244\n",
+ "\\end{description*}\n"
+ ],
+ "text/markdown": [
+ "(Intercept)\n",
+ ": 15.4438313539103AtBat\n",
+ ": 0.0771554748907925Hits\n",
+ ": 0.859115814031969HmRun\n",
+ ": 0.601031069746882Runs\n",
+ ": 1.06369006654778RBI\n",
+ ": 0.879361053365972Walks\n",
+ ": 1.62444616279791Years\n",
+ ": 1.35254779528422CAtBat\n",
+ ": 0.0113499915102498CHits\n",
+ ": 0.0574665439614789CHmRun\n",
+ ": 0.406801566464205CRuns\n",
+ ": 0.114562244309134CRBI\n",
+ ": 0.121165037864304CWalks\n",
+ ": 0.0529920199108252LeagueN\n",
+ ": 22.0914318947081DivisionW\n",
+ ": -79.0403263679412PutOuts\n",
+ ": 0.166199027482507Assists\n",
+ ": 0.0294194957326422Errors\n",
+ ": -1.36092944882302NewLeagueN\n",
+ ": 9.12487766980244\n",
+ "\n"
+ ],
+ "text/plain": [
+ " (Intercept) AtBat Hits HmRun Runs RBI \n",
+ " 15.44383135 0.07715547 0.85911581 0.60103107 1.06369007 0.87936105 \n",
+ " Walks Years CAtBat CHits CHmRun CRuns \n",
+ " 1.62444616 1.35254780 0.01134999 0.05746654 0.40680157 0.11456224 \n",
+ " CRBI CWalks LeagueN DivisionW PutOuts Assists \n",
+ " 0.12116504 0.05299202 22.09143189 -79.04032637 0.16619903 0.02941950 \n",
+ " Errors NewLeagueN \n",
+ " -1.36092945 9.12487767 "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"out = glmnet(x, y, alpha=0)\n",
"predict(out, type=\"coefficients\", s=bestlam)[1:20,]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Lasso\n",
"\n",
"We saw that ridge regression with a wise choice of λ can outperform least\n",
"squares as well as the null model on the Hitters data set. We now ask\n",
"whether the lasso can yield either a more accurate or a more interpretable\n",
"model than ridge regression. In order to fit a lasso model, we once again\n",
"use the `glmnet()` function; however, this time we use the argument `alpha=1`.\n",
"Other than that change, we proceed just as we did in fitting a ridge model."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 117,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Warning message in regularize.values(x, y, ties, missing(ties)):\n",
+ "“collapsing to unique 'x' values”\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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lJak+ZtOx7X9YwL+lzx26MyD2x2pkWLFkUiexnl1bp16w6sagCoBdGoJk/WCy/o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\nSLHV6rrQx7+UlpY2X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+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
"source": [
"lasso.mod=glmnet(x[train,],y[train],alpha=1,lambda=grid)\n",
"plot(lasso.mod)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Perform now cross-validation and compute the associated test error.\n",
"You don't need to create a new split of training/test data.\n",
"But make sure to use again the seed 1 just before running the cross-validation \n",
"to get reproducible results."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 118,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "9.28695474961673"
+ ],
+ "text/latex": [
+ "9.28695474961673"
+ ],
+ "text/markdown": [
+ "9.28695474961673"
+ ],
+ "text/plain": [
+ "[1] 9.286955"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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HfbswN8rPPj920/nOXq3eJxkkCPPw5q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\nTLEzAAAAAElFTkSuQmCC",
+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "set.seed(1)\n",
+ "cv.out=cv.glmnet(x[train,],y[train],alpha=1)\n",
+ "plot(cv.out)\n",
+ "bestlam=cv.out$lambda.min\n",
+ "bestlam"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, refit the lasso on the full data set,\n",
"using the value of λ chosen by cross-validation, examine the coefficient\n",
"estimates and compare them to the coefficients found by ridge regression."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 119,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\t- (Intercept)
\n",
+ "\t\t- -3.04787647701913
\n",
+ "\t- AtBat
\n",
+ "\t\t- 0
\n",
+ "\t- Hits
\n",
+ "\t\t- 2.02551571973406
\n",
+ "\t- HmRun
\n",
+ "\t\t- 0
\n",
+ "\t- Runs
\n",
+ "\t\t- 0
\n",
+ "\t- RBI
\n",
+ "\t\t- 0
\n",
+ "\t- Walks
\n",
+ "\t\t- 2.26853781116777
\n",
+ "\t- Years
\n",
+ "\t\t- 0
\n",
+ "\t- CAtBat
\n",
+ "\t\t- 0
\n",
+ "\t- CHits
\n",
+ "\t\t- 0
\n",
+ "\t- CHmRun
\n",
+ "\t\t- 0.0164710598514274
\n",
+ "\t- CRuns
\n",
+ "\t\t- 0.211773899037458
\n",
+ "\t- CRBI
\n",
+ "\t\t- 0.419446324067207
\n",
+ "\t- CWalks
\n",
+ "\t\t- 0
\n",
+ "\t- LeagueN
\n",
+ "\t\t- 20.4845654335123
\n",
+ "\t- DivisionW
\n",
+ "\t\t- -116.59062077737
\n",
+ "\t- PutOuts
\n",
+ "\t\t- 0.237184593186267
\n",
+ "\t- Assists
\n",
+ "\t\t- 0
\n",
+ "\t- Errors
\n",
+ "\t\t- -0.947399225337244
\n",
+ "\t- NewLeagueN
\n",
+ "\t\t- 0
\n",
+ "
\n"
+ ],
+ "text/latex": [
+ "\\begin{description*}\n",
+ "\\item[(Intercept)] -3.04787647701913\n",
+ "\\item[AtBat] 0\n",
+ "\\item[Hits] 2.02551571973406\n",
+ "\\item[HmRun] 0\n",
+ "\\item[Runs] 0\n",
+ "\\item[RBI] 0\n",
+ "\\item[Walks] 2.26853781116777\n",
+ "\\item[Years] 0\n",
+ "\\item[CAtBat] 0\n",
+ "\\item[CHits] 0\n",
+ "\\item[CHmRun] 0.0164710598514274\n",
+ "\\item[CRuns] 0.211773899037458\n",
+ "\\item[CRBI] 0.419446324067207\n",
+ "\\item[CWalks] 0\n",
+ "\\item[LeagueN] 20.4845654335123\n",
+ "\\item[DivisionW] -116.59062077737\n",
+ "\\item[PutOuts] 0.237184593186267\n",
+ "\\item[Assists] 0\n",
+ "\\item[Errors] -0.947399225337244\n",
+ "\\item[NewLeagueN] 0\n",
+ "\\end{description*}\n"
+ ],
+ "text/markdown": [
+ "(Intercept)\n",
+ ": -3.04787647701913AtBat\n",
+ ": 0Hits\n",
+ ": 2.02551571973406HmRun\n",
+ ": 0Runs\n",
+ ": 0RBI\n",
+ ": 0Walks\n",
+ ": 2.26853781116777Years\n",
+ ": 0CAtBat\n",
+ ": 0CHits\n",
+ ": 0CHmRun\n",
+ ": 0.0164710598514274CRuns\n",
+ ": 0.211773899037458CRBI\n",
+ ": 0.419446324067207CWalks\n",
+ ": 0LeagueN\n",
+ ": 20.4845654335123DivisionW\n",
+ ": -116.59062077737PutOuts\n",
+ ": 0.237184593186267Assists\n",
+ ": 0Errors\n",
+ ": -0.947399225337244NewLeagueN\n",
+ ": 0\n",
+ "\n"
+ ],
+ "text/plain": [
+ " (Intercept) AtBat Hits HmRun Runs \n",
+ " -3.04787648 0.00000000 2.02551572 0.00000000 0.00000000 \n",
+ " RBI Walks Years CAtBat CHits \n",
+ " 0.00000000 2.26853781 0.00000000 0.00000000 0.00000000 \n",
+ " CHmRun CRuns CRBI CWalks LeagueN \n",
+ " 0.01647106 0.21177390 0.41944632 0.00000000 20.48456543 \n",
+ " DivisionW PutOuts Assists Errors NewLeagueN \n",
+ "-116.59062078 0.23718459 0.00000000 -0.94739923 0.00000000 "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "out = glmnet(x, y, alpha=1)\n",
+ "predict(out, type=\"coefficients\", s=bestlam)[1:20,]"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now you should be ready to do the following quiz."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 98,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"IRdisplay::display_html('')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bayesian Interpretation for Ridge Regression and the Lasso (Optional)\n",
"\n",
"Read in the textbook on page 226 about the nice Bayesian interpretation of ridge regression and the lasso and have a look at exercises 7 on page 262."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/src/trees.ipynb b/src/trees.ipynb
index bb284f2..d38c503 100644
--- a/src/trees.ipynb
+++ b/src/trees.ipynb
@@ -1,467 +1,524 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tree-Based Methods"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"New R commands\n",
"- `ifelse(cond, a, b)` take a if cond is satisfied else b.\n",
"- `tree(formula, dataset` fit a tree to the dataset.\n",
"- `cv.tree(tree, FUN = )` perform cross-validation on a tree with loss function FUN.\n",
"- `prune.misclass(tree, best = k)` and `prune.tree(tree, best = k)` prune a tree to have only the best k terminal nodes.\n",
"\n",
"Useful to remember\n",
"- `table(predicted, actual)` creates a confusion matrix (true/false positives/negatives)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting Classification Trees"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The tree library is used to construct classification and regression trees."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"library(tree)\n",
"library(ISLR)\n",
"attach(Carseats)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first use classification trees to analyze the Carseats data set. In these\n",
"data, Sales is a continuous variable, and so we begin by recoding it as a\n",
"binary variable. We use the ifelse() function to create a variable, called\n",
"High, which takes on a value of Yes if the Sales variable exceeds 8, and\n",
"takes on a value of No otherwise.\n",
"\n",
"Finally, we use the data.frame() function to merge High with the rest of\n",
"the Carseats data."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"High=ifelse(Sales<=8,\"No\",\"Yes\")\n",
"Carseats=data.frame(Carseats,High)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now use the tree() function to fit a classification tree in order to predict\n",
"High using all variables but Sales. The syntax of the tree() function is quite\n",
"similar to that of the lm() function. The \".-Sales\" on the right-hand-side means\n",
"that we take all predictors of Carseats except Sales."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tree.carseats=tree(High~.-Sales,Carseats)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The summary() function lists the variables that are used as internal nodes\n",
"in the tree, the number of terminal nodes, and the (training) error rate."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"summary(tree.carseats)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the training error rate is 9%. For classification trees, the deviance reported in the output of summary() is given by $-2\\sum_m\\sum_kn_{mk}\\log\\hat p_{mk}$ where $n_{mk}$ is the number of observations in the mth terminal node that belong to the kth class.\n",
"\n",
"A small deviance indicates a tree that provides a good fit to the (training) data. The residual mean deviance reported is simply the deviance divided by $n−|T_0|$, which in this case is 400−27 = 373.\n",
"\n",
"One of the most attractive properties of trees is that they can be\n",
"graphically displayed. We use the plot() function to display the tree structure, and the text() function to display the node labels. The argument\n",
"pretty=0 instructs R to include the category names for any qualitative predictors, rather than simply displaying a letter for each category."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(tree.carseats)\n",
"text(tree.carseats,pretty=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we just type the name of the tree object, R prints output corresponding\n",
"to each branch of the tree. R displays the split criterion (e.g. Price<92.5 ), the\n",
"number of observations in that branch, the deviance, the overall prediction\n",
"for the branch ( Yes or No ), and the fraction of observations in that branch\n",
"that take on values of Yes and No . Branches that lead to terminal nodes are\n",
"indicated using asterisks."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tree.carseats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to properly evaluate the performance of a classification tree on\n",
"these data, we must estimate the test error rather than simply computing\n",
"the training error. We split the observations into a training set and a test\n",
"set, build the tree using the training set, and evaluate its performance on\n",
"the test data. The predict() function can be used for this purpose. In the\n",
"case of a classification tree, the argument type=\"class\" instructs R to return\n",
"the actual class prediction. This approach leads to correct predictions for\n",
"around 70.5 % of the locations in the test data set."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"set.seed(4)\n",
"train=sample(1:nrow(Carseats), 200)\n",
"Carseats.test=Carseats[-train,]\n",
"High.test=High[-train]\n",
"tree.carseats=tree(High~.-Sales,Carseats,subset=train)\n",
"tree.pred=predict(tree.carseats,Carseats.test,type=\"class\")\n",
"table(tree.pred,High.test)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(89+52)/200"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we consider whether pruning the tree might lead to improved\n",
"results. The function cv.tree() performs cross-validation in order to\n",
"determine the optimal level of tree complexity; cost complexity pruning\n",
"is used in order to select a sequence of trees for consideration. We use\n",
"the argument FUN=prune.misclass in order to indicate that we want the\n",
"classification error rate to guide the cross-validation and pruning process,\n",
"rather than the default for the cv.tree() function, which is deviance. The\n",
"cv.tree() function reports the number of terminal nodes of each tree considered ( size ) as well as the corresponding error rate and the value of the\n",
"cost-complexity parameter used (k , which corresponds to α in the slides and in section (8.4) of the book)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"set.seed(3)\n",
"cv.carseats=cv.tree(tree.carseats,FUN=prune.misclass)\n",
"names(cv.carseats)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cv.carseats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that, despite the name, dev corresponds to the cross-validation error\n",
"rate in this instance. The tree with 10 terminal nodes results in the lowest\n",
"cross-validation error rate, with 50 cross-validation errors. We plot the error\n",
"rate as a function of both size and k."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
"plot(cv.carseats$size,cv.carseats$dev,type=\"b\")\n",
"plot(cv.carseats$k,cv.carseats$dev,type=\"b\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now apply the prune.misclass() function in order to prune the tree to\n",
"obtain the ten-node tree."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"prune.carseats=prune.misclass(tree.carseats,best=10)\n",
"plot(prune.carseats)\n",
"text(prune.carseats,pretty=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How well does this pruned tree perform on the test data set? Once again,\n",
"we apply the predict() function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tree.pred=predict(prune.carseats,Carseats.test,type=\"class\")\n",
"table(tree.pred,High.test)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(92+58)/200"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now 75 % of the test observations are correctly classified, so not only has\n",
"the pruning process produced a more interpretable tree, but it has also\n",
"improved the classification accuracy.\n",
"\n",
"If we increase the value of best, we obtain a larger pruned tree with lower\n",
"classification accuracy:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"prune.carseats=prune.misclass(tree.carseats,best=16)\n",
"plot(prune.carseats)\n",
"text(prune.carseats,pretty=0)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tree.pred=predict(prune.carseats,Carseats.test,type=\"class\")\n",
"table(tree.pred,High.test)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(89+52)/200"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting Regression Trees"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we fit a regression tree to the Boston data set. First, we create a\n",
"training set, and fit the tree to the training data."
]
},
{
"cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\n",
+ "Regression tree:\n",
+ "tree(formula = medv ~ ., data = Boston, subset = train)\n",
+ "Variables actually used in tree construction:\n",
+ "[1] \"rm\" \"lstat\" \"crim\" \"age\" \n",
+ "Number of terminal nodes: 7 \n",
+ "Residual mean deviance: 10.38 = 2555 / 246 \n",
+ "Distribution of residuals:\n",
+ " Min. 1st Qu. Median Mean 3rd Qu. Max. \n",
+ "-10.1800 -1.7770 -0.1775 0.0000 1.9230 16.5800 "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"library(MASS)\n",
"set.seed(1)\n",
"train = sample(1:nrow(Boston), nrow(Boston)/2)\n",
"tree.boston=tree(medv~.,Boston,subset=train)\n",
"summary(tree.boston)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the output of summary() indicates that only four of the variables have been used in constructing the tree. In the context of a regression\n",
"tree, the deviance is simply the sum of squared errors for the tree. We now\n",
"plot the tree."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(tree.boston)\n",
"text(tree.boston,pretty=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The variable rm is the average number of rooms per dwelling.\n",
"The variable lstat measures the percentage of individuals with lower\n",
"socioeconomic status. The tree indicates that lower values of lstat correspond to more expensive houses. \n",
"The tree predicts a median house price\n",
"of 21380 USD for smaller homes in suburbs in which residents have high socioeconomic status ( rm<6.543 and lstat<14.405 )\n",
"\n",
"Now we use the cv.tree() function to see whether pruning the tree will\n",
"improve performance."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cv.boston=cv.tree(tree.boston)\n",
"plot(cv.boston$size,cv.boston$dev,type='b')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case, the most complex tree is selected by cross-validation. How-\n",
"ever, if we wish to prune the tree, we could do so as follows, using the\n",
"prune.tree() function:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"prune.boston=prune.tree(tree.boston,best=5)\n",
"plot(prune.boston)\n",
"text(prune.boston,pretty=0)"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
+ "execution_count": 4,
+ "metadata": {},
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Url7+/fvXv3Ll26XLhwwcnJqZwzvyWK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QUBAbG6ukpOTm5paVlbVr1y7YPPE5LBZr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\nXqPcG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+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ },
+ "text/plain": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
"source": [
"yhat=predict(tree.boston,newdata=Boston[-train,])\n",
"boston.test=Boston[-train,\"medv\"]\n",
"plot(yhat,boston.test)\n",
"abline(0,1)\n",
"mean((yhat-boston.test)^2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In other words, the test set MSE associated with the regression tree is\n",
"35.3. The square root of the MSE is therefore around 5.94, indicating\n",
"that this model leads to test predictions that are within around 5940 USD of\n",
"the true median home value for the suburb."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}