diff --git a/src/lecture1.ipynb b/src/lecture1.ipynb index 3203fb2..7e44dd2 100644 --- a/src/lecture1.ipynb +++ b/src/lecture1.ipynb @@ -1,973 +1,973 @@ { "cells": [ { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "# Lecture 1\n", "## Machine Learning Examples\n", "\n", "Run the following cell with `Shift + Enter` to watch the video." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "## Organization of this Course\n", "\n", "Run the following cell with `Shift + Enter` to watch the video." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "## The Life Expectancy Dataset\n", "Run the following cell with `Shift + Enter` to watch the video." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In this section you will load the life expectancy dataset,\n", "look at it and produce some plots.\n", "You will learn about the `R` functions `file.path`, `read.csv`, `str`, `?`,\n", "`<-`, `$`, `:`, `c`, `pdf`, `par`, `plot`.\n", "\n", "Let us load the life expectancy dataset from the csv file.\n", "You can run the following cell by clicking it and pressing `Shift + Enter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data <- read.csv(file.path(\"..\", \"data\", \"life_expectancy.csv\"))\n", "str(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- We used the function `file.path`, to generate a valid path\n", " in an operating system independent way.\n", "- We used the function `read.csv` and assign the output to the variable `data`.\n", "- In `R` the it is common to use `<-` for (left-)assignment,\n", " but `=` can also be used.\n", "- On the second line we used the function `str`\n", " to look at the names and data types of the columns of `data`;\n", " if you just want to extract the names, you can use the function `names`.\n", "- In `R` the dot `.` does not have any special meaning\n", " and can be used in any variable or function name.\n", "- `R` has usually excellent documentation. You can access it with `?`, e.g." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "?read.csv" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "?\"<-\"" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us actually look at the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "data$LifeExpectancy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- The output consists of a list with the life expectancies\n", " measured in different countries and in different years.\n", "- We can access the data in the columns of `data` by using the extraction\n", " operator `$`. Type `?\"$\"` in the empty field below and have a look at the\n", " examples at the bottom of the documentation.\n", "- We could have also accessed this data with `data[,6]`. Try it out." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us continue to explore the data.\n", "First we look at rows 30 to 40." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "data[30:40,]" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Do you wonder what `NA` means? Look it up with `?NA`.\n", "\n", "With the following command we look at rows 13, 33, 41 and 72." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data[c(13, 33, 41, 72),]" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The combine function `c` is important to know.\n", "You may want to have a look at its documentation\n", "or play with some examples, like" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x <- c(1, 2, 3)\n", "y <- c(4, 5, 6)\n", "x + y\n", "c(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before you move on to the next video, you find in the cell below\n", "the code to generate the figures used in the slides.\n", "The first and the last line are commented out,\n", "such that the plots are shown in this notebook\n", "instead of being printed to the pdf.\n", "Use the documentation, if you want to know more\n", "about the usage of the functions `pdf`, `par` and `plot`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# pdf(\"life_expectancy_example_plots.pdf\", width = 5.8, height = 2.8)\n", "par(mfcol = c(1, 3), cex = .7)\n", "plot(data$GDP, data$LifeExpectancy, xlab = \"GDP per capita [USD]\",\n", " ylab = \"Life Expectancy [Years]\",\n", " xlim = c(0, 100000))\n", "plot(data$BMI, data$LifeExpectancy, xlab = \"BMI [kg/m^2]\",\n", " ylab = \"Life Expectancy [Years]\")\n", "plot(data$Year, data$LifeExpectancy, ylab = \"Life Expectancy [Years]\",\n", " xlab = \"Year\", xlim = c(1999, 2016))\n", "# dev.off()" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "## Error Decomposition and Parametric versus Non-parametric Methods" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "### Artificial Data Generation Process\n", "\n", "With the following code we define the custom function `f`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "f <- function(x) {x^2}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "You may want to look at the documentation `?\"function\"`,\n", "evaluate `f` at different points or create your own function." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "f(3)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In the slides you saw data generated with the following function `myfunc`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "myfunc <- function(x) {sin(2*x) + 2*(x - 0.5)^3 - 0.5*x}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "We will generate `N = 60` data points." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "set.seed(12)\n", "N <- 60\n", "x <- sort(runif(N))\n", "error <- .06*rnorm(N)\n", "y <- myfunc(x) + error\n", "par(mfcol = c(1, 1))\n", "plot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the first line we set the pseudo-random number generator seed to 12.\n", "This means that we will obtain the same pseudo-random numbers,\n", "every time we run the code above.\n", "The functions `runif` and `rnorm` generate uniformly and normally distributed\n", "pseudo-random numbers, respectively. And the function `sort`, well, does the\n", "obvious :)\n", "\n", "You may want to convince yourself that\n", "running the cell above always gives the same data.\n", "What happens, if you remove the first line or replace it by `set.seed(123)`?\n", "\n", "If you feel you don't understand something in the code above,\n", "it would be a good idea to insert a cell below\n", "(you can use e.g. the + button above) and experiment a bit." ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "### Parametric Method\n", "\n", "As an example of a parametric method to estimate the function `myfunc`,\n", "we will fit a linear function to the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "linear.fit <- lm(y ~ x)\n", "plot(x, y)\n", "curve(myfunc, 0, 1, col = 'blue', add = TRUE, lw = 2)\n", "abline(linear.fit, col = \"dark green\", lw = 2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The cryptically looking `linear.fit <- lm(y ~ x)` means simply:\n", "\"fit a linear model with response `y` and predictor `x`\n", "and assign the result to variable `linear.fit`\".\n", "The functions `curve` and `abline` plot the true function\n", "and the fitted line.\n", "\n", "### Non-Parametric Method\n", "\n", "As an example of a non-parametric method to estimate the function `myfunc`,\n", "we define the `kNN` method with three mandatory arguments and one optional\n", "argument with default value `k = 2`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "kNN <- function(x0, x, y, k = 2) { # test point x0, predictor values x, response values y, default k = 2 nearest neighbours\n", " d = abs(x - x0) # compute all distances between the test point and the data\n", " o = order(d) # compute the order of the distances (smallest to largest)\n", " mean(y[o[1:k]]) # take the average response of the k nearest neighbours\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you feel comfortable with the `kNN` function you can skip this paragraph and\n", "move to the next cell. Otherwise, create a new cell below and experiment a bit,\n", "e.g. `tmp.x <- c(5, 2, 3, 1)`, `tmp.x0 <- 1.4`, `abs(tmp.x - tmp.x0)`,\n", "`order(tmp.x)`, `kNN(tmp.x0, tmp.x, c(1, 2, 3, 4), k = 1)`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "grid <- seq(0, 1, length.out = 1000)\n", "y.hat <- sapply(grid, kNN, x, y, k = 1)\n", "plot(x, y)\n", "curve(myfunc, 0, 1, col = 'blue', add = TRUE, lw = 2)\n", "lines(grid, y.hat, col = 'red', lw = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the `seq` function we generated 100 evenly spaced points in the interval\n", "[0, 1]. The `sapply` function lets us apply the function kNN to all values of\n", "grid; from the third argument onward, the `sapply` function passes the arguments\n", "to the function `kNN`, i.e. you can change the `k` to 50, for example, if you\n", "want to see the figure of the slide on the curse of dimensionality.\n", "It is highly recommendable to execute the cell above for different values of `k`\n", "between 1 and 50 and observe how well the curve fits the data.\n", "We call kNN with `k = 1` a flexible method, because it can fit very rough\n", "data with many jumps and kNN with `k = 50` an inflexible method, because it can\n", "fit only rather smooth data.\n", "We will later assess more formally the kNN method with different values of `k`.\n", "If you want to better understand the `sapply` function, it may be worthwile to\n", "experiment a bit, e.g. `tmp.f <- function(x, y) { x + y }; tmp.x <- c(1, 2, 3);\n", "sapply(tmp.x, tmp.f, 2)` or look at its documentation.\n", "\n", "Take a little moment to think about the definitions of the reducible and the\n", "irreducible error as well as parametric and non-parametric methods.\n", "When you are ready, move over to [the quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1088128).\n", "\n", "## Assessing Model Accuracy" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html(' ')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "### Assessing Model Accuracy with Artificial Data\n", "Let us generate a test set with the same generative process as above." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "set.seed(42)\n", "N.test <- 10^3\n", "x.test <- sort(runif(N.test))\n", "error.test <- 0.06 * rnorm(N.test)\n", "y.test <- myfunc(x.test) + error.test" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we compute the training error for the linear model. To do so we first\n", "compute the predicted responses `y.pred`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "y.pred <- predict(linear.fit, data.frame(x = x))\n", "1/length(y) * sum((y - y.pred)^2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "and the test error for the linear model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "y.test.pred <- predict(linear.fit, data.frame(x = x.test))\n", "1/length(y.test) * sum((y.test - y.test.pred)^2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The predict function takes as first argument some fitted model, like the\n", "`linear.fit` we obtained above. As a second argument it expects a `data.frame`\n", "with some values in a column called `x`.\n", "\n", "Let us do the same with the kNN method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "y.pred.kNN <- sapply(x, kNN, x, y, k = 5)\n", "1/length(y) * sum((y - y.pred.kNN)^2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y.test.pred.kNN <- sapply(x.test, kNN, x, y, k = 5)\n", "1/length(y.test) * sum((y.test - y.test.pred.kNN)^2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "As expected, the kNN method has a much lower training and test error than the\n", "linear method.\n", "\n", "Let us now investigate how the training and test errors depend on the choice of\n", "`k`. To do so, we will define the following `assess.kNN` function, and evaluate\n", "it with different `k`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "assess.kNN <- function(k, data.train, data.test) {\n", " x <- data.train$x\n", " y <- data.train$y\n", " x.test <- data.test$x\n", " y.test <- data.test$y\n", " y.pred <- sapply(x, kNN, x, y, k = k)\n", " error.train <- 1/length(y) * sum((y - y.pred)^2)\n", " y.test.pred <- sapply(x.test, kNN, x, y, k = k)\n", " error.test <- 1/length(y.test) * sum((y.test - y.test.pred)^2)\n", " c(error.train, error.test)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "This function takes `k`, a training set and a test set as input and returns both\n", "the training and the test error.\n", "\n", "We will evaluate this function now for different values of `k`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ks <- seq(1, 20)\n", "errors.kNN <- sapply(ks, assess.kNN, data.frame(x, y), data.frame(x = x.test, y = y.test))\n", "plot(ks, errors.kNN[1,], col = \"red\", ylab = \"MSE\", xlab = \"k\", type = \"b\")\n", "points(ks, errors.kNN[2,], col = \"blue\", type = \"b\")\n", "abline(h = 0.0036, lty = 2)\n", "legend(\"bottomright\", legend = c(\"training error\", \"test error\", \"irreducible error\"),\n", " col = c(\"red\", \"blue\", \"black\"), lty = c(1, 1, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We repeat here three important observations we made saw already in the video:\n", "1. The test error is always above the irreducible error.\n", "2. The very flexible method with `k=1` can perfectly fit the training data\n", "(zero training error) but its test error is higher than the one of a less\n", "flexible method, with `k = 5` for example.\n", "3. Training and test error increase with decreasing flexibility of the method." ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "### Assessing Model Accuracy with Real Data\n", "\n", "For real dataset we cannot easily generate an additional test set, typically.\n", "Common practice is therefore to split the dataset into two parts.\n", "We will do this for the life expectancy dataset.\n", "For now, we will only look at the GDP as input and the life expectancy as\n", "output." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "data1 <- na.omit(data[, c(\"GDP\", \"LifeExpectancy\")])" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The function `na.omit` removes all rows where either the BMI or the life\n", "expectancy is not available (na).\n", "\n", "Now we split into training and test set." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "set.seed(199)\n", "idx.train <- sample(nrow(data1), nrow(data1)/2)\n", "data1.train <- data1[idx.train,]\n", "data1.test <- data1[-idx.train,]" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "There are `n = nrow(data1)` data points in total. The first line above samples\n", "`n/2` indices from the indices 1 to n (without replacement). In the second and\n", "third line we extract every row with index occurring in `idx.train` or its\n", "complement `-idx.train` to form the training set `data.train` and the test set\n", "`data1.test`.\n", "\n", "Next we fit a linear model to the training set, define a function to compute\n", "the MSE and compute the training and test error." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fit <- lm(LifeExpectancy ~ GDP, data1.train)\n", "mse <- function(fit, data) {\n", " 1/nrow(data) * sum((data$LifeExpectancy - predict(fit, data))^2)\n", "}\n", "c(mse(fit, data1.train), mse(fit, data1.test))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Interestingly, the training error is higher than the test error. This is an\n", "indication that the model is not flexible enough. This we can also see in the\n", "plot." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot(data1)\n", "abline(fit, col = 'dark green', lw = 2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Instead of linear fits, we could use a quadratic fit." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "q.fit <- lm(LifeExpectancy ~ poly(GDP, 2), data1.train)\n", "c(mse(q.fit, data1.train), mse(q.fit, data1.test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We used the function `poly(GDP, 2)` to form a polynomial of degree 2, i.e.\n", "$$\\beta_0 + \\beta_1 \\mathrm{GDP} + \\beta_2 \\mathrm{GDP}^2$$.\n", "Still the training error is higher than the test error, but they both decreased.\n", "How does the plot look like?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "plot(data1)\n", "grid <- seq(min(data1$GDP), max(data1$GDP), length.out = 1000)\n", "lines(grid, predict(q.fit, data.frame(GDP = grid)), col = 'orange', lw = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hm, also a quadratic model does not seem ideal.\n", "Let us move on to polynomials of arbitrary degree.\n", "To do so we create the function `poly.fit` that takes the degree `d` and\n", "training and test sets as input, and returns the training error, the test error\n", "and the fit object." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "poly.fit <- function(d, data.train, data.test) {\n", " fit <- lm(LifeExpectancy ~ poly(GDP, d), data.train)\n", " c(mse(fit, data.train), mse(fit, data.test), fit)\n", "}\n", "ds <- 1:14\n", "results.poly <- sapply(ds, poly.fit, data1.train, data1.test)\n", "plot(ds, results.poly[1,], col = \"red\", ylab = \"MSE\", xlab = \"d\", type = \"b\")\n", "points(ds, results.poly[2,], col = \"blue\", type = \"b\")\n", "legend(\"topright\", legend = c(\"training error\", \"test error\"),\n", " col = c(\"red\", \"blue\"), lty = c(1, 1))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Here, a polynomial of degree `d = 1` is the least flexible method and it\n", "underfits the data, while the polynomial with degree `d = 14` is the most\n", "flexible method we considered and it overfits the data. We see again the\n", "typical U-shaped curve of the test error: first it decreases with increasing\n", "flexibility, but at some point it starts to increase again. In contrast, the\n", "training error decreases continually.\n", "\n", "Let us look at how well the best performing polynomial (with degree `d = 11`)\n", "fits the data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "plot(data1)\n", "grid <- seq(min(data1$GDP), max(data1$GDP), length.out = 1000)\n", "lines(grid, predict(lm(LifeExpectancy ~ poly(GDP, 11), data1.train),\n", " data.frame(GDP = grid)), col = 'orange', lw = 2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In my opinion, this does not look like coming very close to the true generating\n", "function. The downswing for very high GDPs looks wrong and also the wiggles for\n", "the high GDPs where there is only little data does not look convincing. Maybe we\n", "have to try our luck with other methods.\n", "\n", "Take a little moment to think about the definitions of the test and training\n", "error and the flexibility of methods.\n", "When you are ready, move over to [the quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1088139).\n", "\n", "## Exercises\n", "\n", "**Q1.** For each of parts (a) through (d), indicate whether we would generally\n", "expect the performance of a flexible statistical learning method to be better or\n", "worse than an inflexible method. Justify your answer.\n", "\n", "a) The sample size $n$ is extremely large, and the number of predictors $p$ is small?\n", "\n", "b) The number of predictors $p$ is extremely large, and the number of\n", "observations $n$ is small ?\n", "\n", "c) The relationship between the predictors and response is highly non-linear?\n", "\n", "d) The variance of the error terms, i.e. $\\sigma^2 = \\mathrm{var}(\\epsilon)$ is extremely high?\n", "\n", "**Q2.** Describe the differences between a parametric and a non-parametric\n", "machine learning approach. What are the advantages of a parametric approach (as\n", "opposed to a nonparametric approach)? What are its disadvantages?\n", "\n", "**Q3.** In this exercise you will look at a [Parkinsons Telemonitoring Data\n", "Set](https://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring).\n", "Navigate to that page to find some information about the dataset (if you click\n", "on the link in the previous sentence it will typically open a new browser tab).\n", "You can load the data with the following command." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "data.parkinsons <- read.csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to make progress in progamming in R I recommend you to refrain from\n", "copy-pasting as much as possible.\n", "\n", "We will only focus on the PPE feature and the total UPDRS as a response here.\n", "\n", - "a) Plot the PPE feature against the total UPDRS response.\n", + "a) Plot the PPE feature on the x-axis and the total UPDRS response on the y-axis.\n", "\n", "b) Create a training and a test set.\n", "\n", "c) Fit kNN to the training data for different values of k and compute the\n", "training and the test error. For which value of k do you neither see\n", "underfitting nor overfitting?\n", "\n", "d) Estimate an upper bound for the irreducible error of this dataset." ] } ], "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": "4.0.2" } }, "nbformat": 4, "nbformat_minor": 4 } diff --git a/src/lecture2.ipynb b/src/lecture2.ipynb index c3bb84d..fbf0cb6 100644 --- a/src/lecture2.ipynb +++ b/src/lecture2.ipynb @@ -1,1369 +1,1463 @@ { "cells": [ { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "# Lecture 2\n", "\n", "## Bias-Variance Decomposition\n", "\n", "Please run the following cell with `Shift+Enter` to see the video." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The figure on the first slides was produced with the following code." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "myfunc <- function(x) {sin(2*x) + 2*(x - 0.5)^3 - 0.5*x}\n", "generate.data <- function(N = 50) {\n", " x <- runif(N)\n", " y <- myfunc(x) + .06 * rnorm(N)\n", " data.frame(x = x, y = y)\n", "}\n", "plot.fit <- function(fit, from = 0, to = 1, N = 100, ...) {\n", " grid <- seq(from, to, length.out = N)\n", " y.pred <- predict(fit, data.frame(x = grid))\n", " lines(grid, y.pred, ...)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "With the `generate.data` function we can now generate different (training or\n", "test) data sets.\n", "\n", "We will use the `plot.fit` function to plot our fits. This function has three\n", "optional arguments with default values, and then there are these funny `...` at\n", "the end. They are simply used to pass all other arguments we may provide to\n", "`plot.fit` directly to the `lines` function. Use the help `?\"...\"` to get more\n", "information.\n", "\n", "Now we preform the fits and plot everything." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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n8e33xT8OV//onmzdG0Kd6/F5e0aAFzc/j5oW5dPHyo0G+29PT0s2fP+vv7Hz16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\njBANZVfaIp6o3xJZBqPkMW4ct7r7t9/g66sqQaK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YWewYDEZh2LIFd+8Ky1Wrws9Pvt1HRaFVK9E8UbS8gFcAACAASURBVARMAUYDWQDG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\nx9sW5+XPb5usom3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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# pdf(\"fit_different_training_sets.pdf\", width = 4, height = 5)\n", "set.seed(4)\n", "data.train1 = generate.data()\n", "linear.fit1 = lm(y ~ x, data.train1)\n", "poly.fit1 = lm(y ~ poly(x, 10), data.train1)\n", "data.train2 = generate.data()\n", "linear.fit2 = lm(y ~ x, data.train2)\n", "poly.fit2 = lm(y ~ poly(x, 10), data.train2)\n", "plot(data.train1, col = 'red', xlim = c(.2, 1), ylim = c(.15, .7))\n", "curve(myfunc, from = -.2, to = 1.2, lw = 3, add = T)\n", "plot.fit(linear.fit1, col = 'red', lw = 3, lty = 2)\n", "plot.fit(poly.fit1, col = 'red', lw = 3)\n", "points(data.train2, col = 'blue', new = F)\n", "plot.fit(linear.fit2, col = 'blue', lw = 3, lty = 2)\n", "plot.fit(poly.fit2, col = 'blue', lw = 3)\n", "# dev.off()" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us evaluate the bias and the variance now." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "fit.and.evaluate <- function(formula, x0) {\n", " data <- generate.data()\n", " fit <- lm(formula, data)\n", " predict(fit, data.frame(x = x0))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "This `fit.and.evaluate` function generates a random data set, performs a fit\n", "with the given `formula` and returns the predicted response for input `x0`.\n", "Evaluate the following cell multiple times, to get a feeling for it.\n", "You may also want to try with another `formula` or `x0`." ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "1: 0.507278918135347" ], "text/latex": [ "\\textbf{1:} 0.507278918135347" ], "text/markdown": [ "**1:** 0.507278918135347" ], "text/plain": [ " 1 \n", "0.5072789 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fit.and.evaluate(y ~ x, 0.6)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In the following cell we run repeat the `fit.and.evaluate` 1000 times for two\n", "different formulas and print the results with the `cat` function." ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Linear Method : Bias^2 = 0.01733586 Variance = 0.0003867979 \n", "Polynomial Method: Bias^2 = 4.734845e-08 Variance = 0.0006441321 \n" ] } ], "source": [ "x0 <- 0.5\n", "linear.results <- replicate(1000, fit.and.evaluate(y ~ x, x0))\n", "cat(\"Linear Method : Bias^2 = \", (myfunc(x0) - mean(linear.results))^2,\n", " \"Variance = \", var(linear.results), \"\\n\")\n", "poly.results <- replicate(1000, fit.and.evaluate(y ~ poly(x, 10), x0))\n", "cat(\"Polynomial Method: Bias^2 = \", (myfunc(x0) - mean(poly.results))^2,\n", " \"Variance = \", var(poly.results), \"\\n\")" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "To compute the squared bias above, we needed access to the data generating\n", "function. But usually we do not know this function. Nevertheless, we can\n", "estimate the squared bias by using the error decomposition shown in the slides,\n", "if we know approximately the variance of the irreducible error and have multiple\n", "samples available. Compare the result we obtain in the following cell with the\n", "one we obtained above." ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.0180151938619295" ], "text/latex": [ "0.0180151938619295" ], "text/markdown": [ "0.0180151938619295" ], "text/plain": [ "[1] 0.01801519" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples <- myfunc(x0) + 0.06*rnorm(1000)\n", "mean((samples - linear.results)^2) - 0.06^2 - var(linear.results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please take now a brief moment to think about what you have learned about the\n", "bias-variance decomposition before moving to the\n", "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1093984).\n", "\n", "## The Bayes Classifier and K-Nearest Neighbours Classification" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us create the artificial example from the slides." ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "set.seed(321) # set the random seed\n", "prob.true <- function(x) { 1 / (1 + exp(-10*(x - 0.5))) } # define probabilities\n", "x <- runif(100) # generate 100 uniformly distributed input values\n", "y <- prob.true(x) > runif(100) # generate associated labels" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Do you understand what is happening in the last line of the previous cell?\n", "\n", "With `prob.true(x)` we compute the probablities of label `TRUE` for every input\n", "value. With `runif(100)` we generate again 100 uniformly distributed values\n", "between 0 and 1. With the `>` operator we determine for each input, whether the\n", "probability of label `TRUE` is larger than the randomly generated value; if this\n", "is the case we assign label `TRUE` to that input. Are you convinced that this is\n", "doing the right thing? If not, create a new cell below and run for example\n", "`mean(0.7 > runif(10^5))`, `replicate(10, c(0.2, 0.7) > runif(2))` or\n", "`rowMeans(replicate(10^5, c(0.2, 0.7) > runif(2)))`.\n", "\n", "Let us plot the results from above." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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NnVpInpHADcHu/+AMCtXbqk8eM1fjzjOgDxY2IHAG5t6FDlyKGGDU3nAGAFvAEE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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(x, y, pch = \"|\", yaxt = \"n\") # you can find help about pch and yaxt with ?par\n", "axis(2, at = c(0, 1), c(\"FALSE\", \"TRUE\")) # plots tick labels on the y-axis\n", "curve(prob.true, from = 0, to = 1, col = \"blue\", add = TRUE)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The probability density for class label `TRUE` is equal to 0.5 for x = 0.5,\n", "smaller for smaller x and larger for larger x. Therefore the Bayes Decision\n", "boundary is at x = 0.5. The Bayes Error Rate can thus be computed by integrating\n", "the probability density function from 0 to 0.5 and multiplying the result by 2,\n", "because we predict as many FALSEs incorrectly as we predict TRUEs incorrectly.\n", "The result is $\\frac2{10}(log(2) - log(1 + e^{-5})$.\n", "We can also estimate the Bayes Error Rate with many samples." ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "data": { "text/html": [ "0.137313" ], "text/latex": [ "0.137313" ], "text/markdown": [ "0.137313" ], "text/plain": [ "[1] 0.137313" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x <- runif(10^6)\n", "p <- prob.true(x)\n", "y <- p > runif(10^6)\n", "y.pred <- p > 0.5\n", "mean(y != y.pred)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Does your estimation reach approximately the same result as the theoretical\n", "prediction above?\n", "\n", "Let us create now an artificial two dimensional data set." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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4iiY2FH9FEOHz6ckZERHBx88uTJJk2avO+yHj2weTP+XXQtXQpbW7i6/v11fv57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\nPy555r5ec6IM3uMmDdSZpkoAA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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "bayes.boundary <- function(x) {(6*x - 9)^3/160 - (5*x - 12)/2.5}\n", "prob.true <- function(data) { 1 / (1 + exp(-5*(bayes.boundary(data$X1) - data$X2))) }\n", "set.seed(9)\n", "N <- 200\n", "x <- data.frame(X1 = 3*runif(N), X2 = 3*runif(N))\n", "y <- prob.true(x) > runif(N)\n", "plot(x[y,], col = 'blue', xlim = c(0, 3), ylim = c(0, 3)) # plot all points with class label TRUE\n", "points(x[!y,], col = 'red') # !y means \"not y\", i.e. select all points with class label FALSE\n", "curve(bayes.boundary, from = 0, to = 3, lty = 2, add = T)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "We will use again the `kNN` function to perform classification, this time with\n", "the Euclidean distance in 2 dimensions to find the nearest neighbours." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "kNN <- function(x0, x, y, k = 2) {\n", " d = sqrt((x[,1] - x0[1])^2 + (x[,2] - x0[2])^2) # Euclidean distance in 2D\n", " o = order(d)\n", " mean(y[o[1:k]])\n", "}\n", "grid <- expand.grid(X1 = seq(0, 3, length.out = 100), X2 = seq(0, 3, length.out = 100))\n", "prob.estimated <- apply(grid, 1, kNN, x, y, 5) # 5 nearest neighbours\n", "y.pred <- prob.estimated > 0.5" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In the third to last line we created points that lie on an evenly spaced grid.\n", "In the second to last line we use the `apply` function along dimension 1 (rows) of the\n", "grid, to compute the estimated probability for all points on the grid.\n", "You may want to run `tail(prob.estimated)` and `prob.true(tail(grid))` to see\n", "how well the estimated probablities match the true probabilities.\n", "In the last line we compute the predicted class labels by applying the Bayes\n", "Classifier to the estimated probabilities.\n", "\n", "Let us plot everything." ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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R8di/u0bIGLMiSm02qNHzNJ7YK1h+Ax49V+sv+HqooVcfH481it9HkPQzqiYsW8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kQoAtTh1EZg14ZSA5tySWe2nv6ClTKsQKVwOS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\ngxYNuZkUk6GkF9mGdA8IsF++vCXpQbYnPcgQ0oIqGPkWG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10ltr3E21WrvjQzK5o5888rV65lZ39x6VL3KVNWmJoWb978bWW19+wZNnv2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\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I68nRpbZlhTxZYZxXtCQpVy5cK1Za6u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\nahEREcCxz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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(grid[y.pred,], col = 'yellow', pch = '*', xlim = c(0, 3), ylim = c(0, 3))\n", "points(grid[!y.pred,], col = 'green', pch = '*')\n", "points(x[y,], col = 'blue')\n", "points(x[!y,], col = 'red')\n", "curve(bayes.boundary, from = 0, to = 3, lty = 2, add = T)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "You can see that the kNN decision boundary (the Bayes decision boundary based on\n", "the estimated probability density; boundary between green and yellow areas)\n", "follows the Bayes decision boundary of the data generating density not perfectly\n", "but captures the main trend.\n", "\n", "Let us compute the training and the test error." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.09 \n", "test error: 0.137 \n" ] } ], "source": [ "training.error <- mean(y != (apply(x, 1, kNN, x, y, k = 5) > 0.5))\n", "cat(c(\"training error: \", training.error, \"\\n\"))\n", "N.test <- 10^3\n", "x.test <- data.frame(X1 = 3*runif(N.test), X2 = 3*runif(N.test))\n", "y.test <- prob.true(x.test) > runif(N.test)\n", "test.error <- mean(y.test != (apply(x.test, 1, kNN, x, y, k = 5) > 0.5))\n", "cat(c(\"test error: \", test.error, \"\\n\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Once you feel ready, please head over to the [quiz]()." + "Once you feel ready, please head over to the [quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1094719)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assessment of Binary Classification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us go back to the simple artificial classification example and compute the\n", "confusion matrix." ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A matrix: 2 × 2 of type int
42 4
747
\n" ], "text/latex": [ "A matrix: 2 × 2 of type int\n", "\\begin{tabular}{ll}\n", "\t 42 & 4\\\\\n", "\t 7 & 47\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 2 × 2 of type int\n", "\n", "| 42 | 4 |\n", "| 7 | 47 |\n", "\n" ], "text/plain": [ " [,1] [,2]\n", "[1,] 42 4 \n", "[2,] 7 47 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "set.seed(321)\n", "prob.true <- function(x, b = 10) { 1 / (1 + exp(-b*(x - 0.5))) }\n", "x <- runif(100)\n", "y <- prob.true(x) > runif(100)\n", "y.pred <- prob.true(x) > .5 # decision threshold 0.5\n", "TP <- sum(y.pred[y])\n", "FP <- sum(y.pred[!y])\n", "TN <- sum(!y.pred[!y])\n", "FN <- sum(!y.pred[y])\n", "matrix(c(TN, FP, FN, TP), 2, 2)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Instead of computing the true/false positives/negatives manually, we could have\n", "used the function `table`." ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "data": { "text/plain": [ " y\n", "y.pred FALSE TRUE\n", " FALSE 42 4\n", " TRUE 7 47" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(y.pred, y)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Play a bit with different values of the decision threshold and observe how the\n", "confusion matrix changes.\n", "\n", "Next we will compute and plot the false positive rate, the false negative rate,\n", "the true positive rate and the error rate." ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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Syh2HGLsTHV1lIhVlsDCI2DicPhqYdXv7161clVPot9zqWfY50IQIAKCkgkIiMj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\nw+SfJuc8zGGdC5QnLY2IyM6OdQ4uQbHjMEdHun2bystZ5wAA4C6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lqqio+P/HOrq6RJr/PbJQIpH843lNTHAwnT7NOgQAAHCOWCTeOHJj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Td196mJr+oapPBWVsWiDqQWAKOwDDh0NW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\nemTT2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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "x <- runif(10^4)\n", "y <- prob.true(x) > runif(10^4)\n", "error.rates <- function(threshold, x, y) {\n", " y.pred <- prob.true(x) > threshold\n", " TP <- sum(y.pred[y])\n", " FP <- sum(y.pred[!y])\n", " TN <- sum(!y.pred[!y])\n", " FN <- sum(!y.pred[y])\n", " c(FP/(TN + FP), FN/(TP + FN), TP/(TP + FN), (FP + FN)/length(y))\n", " }\n", "thresholds <- seq(0, 1, length.out = 100)\n", "result <- sapply(thresholds, error.rates, x, y)\n", "plot(thresholds, result[1,], type = 'l', col = 'red', ylab = \"error rate\", xlab = \"decision threshold\")\n", "lines(thresholds, result[2,], col = 'blue')\n", "lines(thresholds, result[3,], col = 'darkgreen')\n", "lines(thresholds, result[4,])\n", "legend(\"center\", legend = c(\"false positive rate\", \"false negative rate\", \"true positive rate\", \"error rate\"), col = c('red', 'blue', 'darkgreen', 'black'), lty = 1)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us now plot the ROC curve." ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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IbVpuPH5Ztv5IsvJH/+3A8GADyj1NTUAQMGjBkzRnUQaIcJTOyk1NBfvl77ymer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\nHUuxJubyZXFzExcX1TkA4DF16tTZv39/XVYTANUodibmyhUpX15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Kof9ZlClTWiQ0NFTEST/ZzFpkpLiaw91wAfw/p06dioqKWrlypeog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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(result[1,], result[3,], type = 'l', col = 'blue', ylab = \"True positive rate\", xlab = \"False positive rate\")\n", "abline(c(0, 0), c(1, 1), lty = 3)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Instead of computing the error rates we could have used the `ROCR` library.\n", "Note that we have to provide the predicted probabilities and the class labels to\n", "the `prediction` function below." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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tcueXurVSvTOQAAgMtR7Ozmww/VtKnKlDGdAwAAuBzFzm7y8tSzp+kQAADABIqd\nrWRlafNmlS1rOgcAADCBYmcrO3fqyBHdeKPpHAAAwASKna0kJ8vDQzVrms4BAABMoNjZysGD\nqlxZnvxTBQCgVKIC2EdhoaZOVWio6RwAAMAQL9MBUGI2btSaNZozx3QOAABgCDN29vHMM6pf\nX126mM4BAAAModjZx4oVGj5cFSqYzgEAAAyh2NnEzz/r2DF17Gg6BwAAMIdiZxNPPKH27RUb\nazoHAAAwh2JnE8nJuuEG0yEAAIBRFDs7SErSjh2qX990DgAAYBTFzg5mz1ZYmFq0MJ0DAAAY\nRbGzvJwcTZ2qdu3YmhgAgNKODYot78MPtWOHPvzQdA4AAGAaM3aWN3u2hgxR69amcwAAANMo\ndtaWm6stW9SunekcAADADVDsrG3zZqWmqlMn0zkAAIAboNhZ2/ffy99ftWubzgEAANwAxc7a\nvv9e/fvLw8N0DgAA4AYodta2dauaNzcdAgAAuAeKnYWdPq2DB9WggekcAADAPVDsLCw+XpKi\now3HAAAAboJiZ2GrVysoSNWrm84BAADcA8XOwuLj1ayZvL1N5wAAAO6BYmdVWVmaPl1165rO\nAQAA3AbFzqri45WUpHHjTOcAAABug2JnVfHx8vJSRITpHAAAwG1Q7Kxq5kw1by5/f9M5AACA\n26DYWdKpU1q2TMOGmc4BAADcCcXOkubN04kTuv560zkAAIA7odhZ0o4dathQkZGmcwAAAHdC\nsbOkjRvVpInpEAAAwM1Q7Czp11/VsKHpEAAAwM1Q7KwnI0MpKWrUyHQOAADgZih21rN7twoK\nFB1tOgcAAHAzFDvrmTZN9eqpRg3TOQAAgJuh2FlPTo6aNZOHh+kcAADAzVDsrCclRT4+pkMA\nAAD3Q7GzmBMn9PXXatnSdA4AAOB+KHYW89tvys7WwIGmcwAAAPdDsbOYggJJCgkxnQMAALgf\nip3FHDigkBDenAAAAEWg2FlMXp6Cgih2AACgCBQ7i/nuO4WHmw4BAADcEsXOSo4e1RdfaNgw\n0zkAAIBbothZyfHjyspS376mcwAAALdEsbOSgwclydvbdA4AAOCWvIo9suBk8p49B1JPeFW5\nslmEZ443hx+43rffqkkTValiOgcAAHBLxZmxy/z9o/u71S4fEnFFk5ZXtb1teqKWjqhe+8aX\nV6Y5PR7+Ytky1avHK7EAAKBoDotd/paXu7UZPnFJYlCLPkO71z3zFLBSrcgjX4ktnCIAACAA\nSURBVDzcqe3YFaecnhBnnTypjRt17bWmcwAAAHflqNilTHvwiVVq+chPCQlrFswY1erM89dm\n49dsnNi17LbXxk7Z5/yMkCTt2KGsLHXoYDoHAABwVw6KXfrCz3/Iibz79efbV/zrSK+YkRPu\njCxcu2RphhPT4RzjxqlqVUVEmM4BAADclYOXJ1IOHy5UVHR0Ef3Po0aNGOnw4cNSkHOy4U+n\nTunnn/Xee/Iq/usuAACglHFQEyKiorz0w6pVGff3/3t7K9y1K14ejcIqOC3b3+Sk7YlL8m3Y\nIPLMOr/TCcs//+KH3xPScspWqtO61429m1W0cefZsUO5uerUyXQOAADgxhw8ig3oNbhPcMac\n+wa/sTa14Jzr+amrnhz3bpJv+369yjs13xlZ2+c80Klm5ZrNH/gqXZJytk/tV692h6GjJ7z8\n5sT/vvjEyH7NoxsMeOu3TBdkMWPfPvn5qXJl0zkAAIAbczTJFTrgv5M/X3vznIda13i9eWyl\n1GydmHd/76+3L1+990RAu1cm3hHp/IyZS0Z1GfT+If+a19xxU4tyUv76CTeOnL/Pq1qHEffc\n0rlBeH7K1mUz3/7w01GdT/lvWXibLXd527dPVaqwNTEAALgQx08vqw36eF2lK8eOe2Xuhh/2\nS9JvXy+SX7UOoyZNenFYQxc0jazF78085Nlg9LerX20bKCn/u7ff3ppfZeCn6z7pV+nMkL6D\n7rzz2uEt+n701Ou/3PZyK+dncrmCAgUHmw4BAADcW3GWpXlGdBo3a/2YKYlxm3YlncjzDYms\n07he5bKu2iY3MT4+W/UG3dU28Mz3h+LijivkxuH/a3VnhPW556aqH72yZs1BtXLBLCIAAIDb\ncVDs8k4eTc30Cq0U7CvPgKqNrq7a6M97BafSUjLKhFQO9nNuxKCgICk9O/t/3wcGBUll/f3/\nPs7Ly0vK/nOcrZxiJ2gAAOCIg5cntr/SIaL6vUuKvHd8Zv+IiL7vJjkh1V9UvOrqmto99alp\nCXmSpJCu17bxTlr46crT5446veaTLxMU2rRplLPzGJGSoqpVTYcAAADuregZu7S1sz9ee1RS\n0to05e9cNGlSwt+HFJ7aNHOd1DAnx8kJpWZjXrnlwxtn3HFlyx/Hjrurf/dWI99+6YtOY/v3\n8n/12WHtaofnH96y5P2nnnhzm0/z5x68xp57npw+zZsTAADAgaJr0KHF/7lvQtz/vkuafN+6\noj/t1/z67tWckusvQq+ftvqzsJvvfWvG+CEzxssrsFJkeU/v5GUv3dzupT8G+dcdPuuLx+o7\nPPzWmpKTFR1tOgQAAHBvRRe7aje8MKPWcUmJnz/22MKoMR/c0/TvQzy8ylWsd1WHJpVd0qTK\nVOv32vJrx67+7JOvlv28au2WvYfTvP28cvO9/YMqVL2iUWynvrfcfes10WVdkcWIY8dUp47p\nEAAAwL0VXeyCG/ce2liS9mR9Pf/oFf2GDm3j0lRF86ly1ZDRVw0ZbTqHy2VkaNUqjR1rOgcA\nAHBvDubbatw5a81PT5+n1f02aUi/Cd+dLPlQ+KvsbBUUqFYt0zkAAIB7K8arBnmHfv549vc7\nUrPyC8+9XHh682dzF5dvcvipbgHOSgdJUl6e6QQAAMAKHBa7lE8GNxv8WUqR9zzLt7+/d0yJ\nZ7o0n/T3GDxPDZ7avOXphsX/1N69e1u1apV3wep0Zm+8wsLCC4xxqsRESapY0dTPBwAA1uCo\n2O147/nPUsKvefrdp7t5f/vYgP+cHLVo0nX+x3b+8M7TL+64ft7CBxpY+zXU6tWrz50798LF\nbuHChf/97389PFx11MY/nKmU5cqZ+vkAAMAaHBS7jJU/b1atJ1556romUoOhrZ8duSej6VU9\n/K5q3721/9WN7powZNsrse6xc1z/mSd6f6gyPv84keKCPD09O3bseOEx8fHxlx6rJOzcKT8/\n9rEDAAAOOJhvS0lJkaLP7qAWEh0dnLt5844zH6xz110d4j+YutRd1n95+QUEBASU9bH2DGKR\n9uxRw4YUOwAA4ICD2bbw8HBp74EDUrDONLwZ27fnqom3pNCoqMBjmzcnqnu0C4JKUmFW8pY1\nq3/dtifxSMap7AIvv4DQytVq1mveKrZuuK+LMpiwYYOquWAfaAAAYHEOil1wh07NPL+ZNPaV\nHtPubRVRo3nzkJz5H396eMCQSh45G39claFqQUEuyZkZN/OJB5967/s9Re2u4hlYq/MtD/9n\nwh0tw2w4Xydt36577jEdAgAAuD1H6+Nq3f3MrW/1nTbuqqgN83Nnd715UJVpk29reuWMlmEJ\ny5ds92tzb9fyzg95eu1THTo8syHLK6Rmq2vbX92sRqXyoaFBfsrNyjyWnLhn69ofv1/69t1L\n538zbfmcW2u6x5K/kpSergC2lAEAAI44bEEhvd9b/0vn9z75ObSq5N/l+dnP7B444ftvFkhB\nTe7+6KN7XLDbyd63731ug1fLcd/Oe7Zb1SIfuRam/zZ1eN97Ph8x4qMeS+6o5PxILpSQoCNH\nFBVlOgcAAHB7xZje8gyPHfpY7NAz34S2f3JJ4uikPQeyw2tEh/g4N9wZR7/7Zn1BxP2vvNCt\n6vketHoEN/3XzNeXVe7/ybxFGXfc7pqnwy7y6qsqX15t3OFMNwAA4N4crElL/On9SZNmrU37\ny8Uy5SKuqOuiVicpPT1dCqtUyUHUcrVqVZaOHDnimlQus22bevViEzsAAOCYg7bk8duH9933\n8JwdrglTtGq1a/tp67zZm3IuNCpv85eL98qvVq1IV+Vykfh4xcaaDgEAAKzAQbGL7DPgar9D\nX3/+S5Zr4hTF+9r7761VsHFC5/b/emPBhgMn8/96uyDz0OZv3xnVsfPTGwur33lPbz8zKZ0m\nI0MuevMYAABYnKM1dtEjZs3Y3Ou2vt3ynntyWMd6EYF/+4B3QFiFACe/h+rd8v++/Tj12js+\nmvrQdVMf8vQLrVKtSligv7dH9smMjLSkA4dP5kvyq3XT1PmvtLfXfnarVystTU2amM4BAACs\nwEEn2/JMs0YT4iTpjbu7vVHEgAZPbd7ydEMnBPsL7xqDPtzc5d45U97/fMmKVeu374pLPHvH\nwyekWtNr2vfoP3zEsC7Vyzo7iKtt3apq1Sh2AACgWBwUu5CGPQcOvFBvq9YwpETznJ9XeOzN\nT8Te/ISkgtzM9GPHM3M9/QJCywf72XJT4jMyMuRrrzlIAADgPA6KXdX+L3/S3zVJLoKnd7nQ\niuVCTcdwgR07VKuW6RAAAMAibDzbZQdxcape3XQIAABgERQ793XihFauVI8epnMAAACLoNi5\nr+++U2GhWrQwnQMAAFgExc59TZyozp1VtarpHAAAwCIodu4rJUW9epkOAQAArINi56aOHNGe\nPYqONp0DAABYR/EPjSg4mbxnz4HUE15VrmwW4Znj7ePjxFhYvVoeHurZ03QOAABgHcWZscv8\n/aP7u9UuHxJxRZOWV7W9bXqilo6oXvvGl1emOT1e6VVYKF9f+fubzgEAAKzDYbHL3/JytzbD\nJy5JDGrRZ2j3ut6SpEq1Io988XCntmNXnHJ6wlIqO9t0AgAAYDWOil3KtAefWKWWj/yUkLBm\nwYxRrc48f202fs3GiV3Lbntt7JR9zs9YKm3apJgY0yEAAIClOCh26Qs//yEn8u7Xn29f8a8j\nvWJGTrgzsnDtkqUZTkxXimVm8uYEAAC4OA6KXcrhw4WKio4uYphHjRox0uHDh50TrLRLTFRA\ngOkQAADAUhwUu4ioKC/FrVpVxLRc4a5d8fIIC6vgnGClXW6uwsNNhwAAAJbioNgF9BrcJzhj\nzn2D31ibWnDO9fzUVU+OezfJt32/XuWdmg8AAADF5Ggfu9AB/538+dqb5zzUusbrzWMrpWbr\nxLz7e3+9ffnqvScC2r0y8Y5Il8QEAACAI473sas26ON13780pHnZQxt+WLcvT2m/fb1oVVJI\n+1EfrfpmTCNvF2QslY4flyfHggAAgItRnJMnPCM6jZu1fsyUxLhNu5JO5PmGRNZpXK9yWQ+n\nhyvNNm3S8OGmQwAAAEtxUOz2fjL+ndTWQwf2bBzuHVC10dVVG7kmVilXWKicHFXgvRQAAHAx\nHDzty9y+4OX7rmtSJaJx75Evzl55gIMmXOLYMWVmKizMdA4AAGApDordFXdOnfF/o65r6rtr\n0TuPDmlbvVKNjrc++d5324/nuyZeKVVYKIl97AAAwMVxUOx8q1499NGJ89clHklY+cmrD93Y\nqGD9jOfu6l6vctUWNz70+hcbknNcE7OUSU01nQAAAFhQMV+89AiofvXA0a99uirhyIG18958\n+Mbax79/c/QNLaq2eXGncwOWSps2qVw5jhQDAAAX56J31PANrlg5IrJqVFR4gIeUf/o0c3Yl\nLz9f/v4KDDSdAwAAWEpxtjuRpKzk35Z+9eX8+fO/Wvrb4WypTHDtjrc+NWTIzTfWd2q+0unr\nrxUTYzoEAACwGgfFLvvAz3M//vTLL7/8Zs2+zEJJfpGxN44eMmTIoGuvrOzrkoSlUXKyOnQw\nHQIAAFiNg2K36/0RwybESWVC63UbPHjwkCE3dKgZxIEIzrZunfr2NR0CAABYjYNi5xvRcuDY\nfw0ZMrBns4qcHuYaubk6eVK1apnOAQAArKaIYpd/6vixU3ll/ENC/b1q3PLapFN5ktLPswOH\nl39oiH8Z52YsZY4cUW6uqlQxnQMAAFhNEY9Vt73UNjw8PPaZ3/74+gLavrTN5Zlt7vffJSko\nyHQOAABgNUXM2AXV7nDttdFV6oX88fUFPl+9NgWkhKWlqUoVVa9uOgcAALCaIopd1JC3Fg4p\n4mu4jIeH6QQAAMCCHLzhmnfyaPLh9Owi7xWcSktOTs9yQqjSLSGB57AAAOBSOCh221/pEFH9\n3iVF3js+s39ERN93k5yQqlTbu1d165oOAQAALKjo7U7S1s7+eO1RSUlr05S/c9GkSQl/H1J4\natPMdVLDHI4UK2GHDysiwnQIAABgQUUXu0OL/3PfhLj/fZc0+b51RX/ar/n13as5JVcpduoU\nxQ4AAFyKootdtRtemFHruKTEzx97bGHUmA/uafr3IR5e5SrWu6pDk8qcQ1HCkpLk7286BAAA\nsKCii11w495DG0vSnqyv5x+9ot/QoW1cmqr02rlTO3eqXj3TOQAAgAU5OHmi+pC3Fl6fp9Tz\nnDvByRMl7eBBFRSoRw/TOQAAgAVx8oR7KSyUJB8f0zkAAIAFcfKEe4mPV2io6RAAAMCaOHnC\nvSQmqk4d0yEAAIA1Xfw7rYWnEn9b/uPPm5M4c8IJTp5U2bKmQwAAAGsqRrFLXf3fO7s0vHFK\nkqTCPe9ff0V0sw6d2zWOiu707M/HnB6wlNm4UQ0amA4BAACsyVGxK4h7vmfnB99fleYT4C1l\nLXpm7IJDgbHDxz96a9PcZf++4YHFmS6JWWrk5aliRdMhAACANTkodvlL33x1fW6j8cv3zr45\nTPlL53153LPNs/On/ef/Plw6ZWDgkTnTv852TdBS4uBBBQaaDgEAAKzJQbFL3LQpTQ0GD4/1\nlaRff/zxuJr17l1FkoK6dIlVTnx8ovNDlhZ5edq3TzVrms4BAACsyUGx8/DwkELPbsBxYMWK\nfaresWP0mXunT5+WCs9svIaSUFioggK2OwEAAJfIQbGrWru2vzb9/HOGlPPbux+tU/nu3WPP\n3Er+bslmeUdHRzo/JAAAABxzUOw8e4y6p9axWTc3bNGqYcfnfi+MGjKsYxml/zb7uVt7PLDw\nZHDfQT3YnAMAAMAtOHor1qvFs1+8P7xBzua1u05VavfUjGfbeEsH5k94cvqOCn1eWDilf4hL\nYpYOPNYGAACXo4iTJ/6mbMPbp629/b2s0wW+Zb09JEnVBn+wekjd5rXLc6Rpidq0SZLCwkzn\nAAAA1uS42J1RpkzWnvVr4pMz8nxDI69o3LJ1SHE/iWLbtEkVKnCkGAAAuETFqWfHVr1+74hn\n52w+VvC/K2XKN+xz77Mvj7++lp8Ts5U6+/YpIsJ0CAAAYFkOi132hqe7dpmwISewRoebOjeK\nCvU6mZIQt3zJyvnP9vvp5/+uWHJ/gzKuyFkq/PqrWrY0HQIAAFiWo2KX+P5Dz2/wbPno8sXP\nt6ng8b+rhZm7Fzxy06C3Hnnww4FL7qjk5IylRkKCWrUyHQIAAFiWg7dij32z4Ofcire9+Nw5\nrU6SR7la1705aURk1o8Lvjvp1HylR2Gh9u1TTIzpHAAAwLIcFLsjKSmFqlm7dhGPWz3r1aut\n/IMHk50TrNRJSFBGBm9OAACAS+eg2IVXrOihhL17i9pgbf/+/VJAQIBTcpU+mZmSVL266RwA\nAMCyHBS70B592ngnvTv236vTCv5y4/S2iY9Ojledjh0qOzFdaZKbazoBAACwOEcvT1S9641/\nT+/w5HNtomZ1urFfuwbVw31PHY7fuOiTLzYeKYgaPu2BRi6JWQokJsrPT8HBpnMAAADLcrjd\nic+VT3z3U9iYEU9N/2H6az/8cdmvauexb77/fJ9Qp6YrTQoL5e0tb2/TOQAAgGUVZ4Pi4CtH\nvLfu9he3r1316+7k9ByvkCq1r2zT6opQzp4oSQcOKJSaDAAALkNxy1l+9qlTeZ6+/sHhFYIr\nVouKCKbVlbD8fIWEmA4BAACsrBj9LHvPp+PvGvP2DweyzvlYWPNBj7z66piOFT3O/0FcjDNv\nxQIAAFwyh8Uuec4tbQd/mlSmYtPrbunavEaY96mUA/Ebv/7ix5njuv2yf/HGN69hv5MSceSI\nqlUzHQIAAFiZg2JXsPLF0Z8mhXR66ccF45qc0+DyUn56ss+1L7z14BsjtjxR37kRS4nCQnnx\nfBsAAFwGB/vY7Vu16pCi7nxhbJO/zst5Vezw/Jv3RBXELVue6sR0pcn27ayxAwAAl8VBsfP3\n95cqR0QUsZLOIyqqqnT69GnnBCt19u1TIzYFBAAAl8FBsavUs09smS0//JDyz1sZK1duVnTb\ntpHOCVbqHDyoqlVNhwAAAFbmoNipxr1T/u/Kn0d1u3vqj3vS885ezDsWN//Jvvd8GXXf5Edj\nHf0KKIZvv9WJE6pRw3QOAABgZQ6W6+96s99NUxKUdeDdf3V+956y5StXCvXLT08+lHoqX/IN\nnntrvbl/Dq479qdlY+s4N69NbdummBjFxprOAQAArMzRe5ieXl5e/pVq1ql0zrUK1WpVKGps\nkB+zd5foxAmVL286BAAAsDgHxe6KUQu2j3JNklJt+3ZFRZkOAQAALI45NreQlqaaNU2HAAAA\nFkexcwv796tCkY+3AQAAio1i5xYKCxUUZDoEAACwOIodAACATVDsAAAAbIJiZ15eno4fl0cR\nx7YBAABcBEf72P2p4GTynj0HUk94VbmyWYRnjrePjxNjlSqpqUpKUrNmpnMAAACLK86MXebv\nH93frXb5kIgrmrS8qu1t0xO1dET12je+vDLN6fFKkeBg0wkAAIDFOSx2+Vte7tZm+MQliUEt\n+gztXtdbklSpVuSRLx7u1HbsilNOT2h/hYWmEwAAAFtwVOxSpj34xCq1fOSnhIQ1C2aManXm\n+Wuz8Ws2TuxadttrY6fsc35Gu9u/XxJHigEAgMvloNilL/z8h5zIu19/vn3Fv470ihk54c7I\nwrVLlmY4MV3pcOiQfHwodgAA4HI5KHYphw8XKio6uohhHjVqxEiHDx92TrBS5PRphYXJq/jv\nsQAAABTFQbGLiIryUtyqVUVMyxXu2hUvj7AwwydhZR2KW79+Z2q+2RQAAADmOSh2Ab0G9wnO\nmHPf4DfWphaccz0/ddWT495N8m3fr5fhJ4i7pw6MjR05/4TZFAAAAOY5ev4XOuC/kz9fe/Oc\nh1rXeL15bKXUbJ2Yd3/vr7cvX733REC7VybeEen0iDmpe/ekZp/v7t7UHOlU8q7t2wMlyTes\nRkyYxXbYy8oynQAAANiC44Vd1QZ9vK7SlWPHvTJ3ww/7Jem3rxfJr1qHUZMmvTisobfTE2rn\npD6NJsRdcMiuJ1vWe1KS1OCpzVuebuj8UCUpKUmRzu/HAADA9oqzYt8zotO4WevHTEmM27Qr\n6USeb0hkncb1Kpd11RFYVTvd1G7y9hWH8z0rNOvdo37gX++mb1q4cHO5trf0rOMjSZHNLfly\nKcd4AACAy1f8VzE9A6o2urpqIydmOY+QDk/9tLXnWw/c/tjMLb8e6fXOlCevjfb94+6Wpxsu\n3Fz51jffuzPE9dEAAADciINid2Du6Ifm7r/AgKgBr782oFqJRiqCR/mWo2Zs7DP4P3f96/96\nN/xs0LPvvflA2/DiHIdmBQcOmE4AAABswUGxS9/63bx551nf5unlXUb1m0wo+VBF86nea8J3\ncTd+MO72MWPa1/tkxGvvvTCsUZCrfroTxcerRQvTIQAAgPU5mPWqO/anpL84uG9X3NrvZr1w\nZ8sK5RqM+Dzh1ycbuCboWUGNb5/yS9z3z7dJnXbrlfW7P7Eg4bzvy1pJYKDjMQAAABfmYMbO\nK6BC5YC/XasSVat+bNf+3Su3bD7k7thdi26p5LR0RStTpfOjX27u98njd9z3f9dd71FGquzi\nBCXrBJvwAQCAknDJ69R8mg69qcGJxXO+NtRK/OsMen351p/fvK1Hxy5dmke6YNsVp0lNVTWn\nL1MEAAD2dxkHlB4/flzyO5wimXqO6Bl+1X3vLrzP0E8vSWXKmE4AAACsz0GxK8g5fSrnH+ew\nFuZm7P950pj3EuXf7gq21r0sJ0/q8GH5+joeCQAAcGEOit3W52MvcOqDb6PxD13rV9KRLtGW\nuU9/tlUVO44c2bFi8T9VUFCwfPnyvLy8C4zZtm3bZac7r7Q0nTyp1q2d9xMAAEBp4aDYlYuO\n7dAh7O9XPbzKBle6ovV1d48c0NBtppq2zJ0wYZ4aqP9FFbt9+/YNGDDgwsUuOztbUmFh4eVG\nPD9Pu+zJBwAADHJQ7Lxj2vbvf03LITe3dPuTuur2HTMmWhFX/6OGXlBMTExKSsqFx0yZMmXE\niBEeHq46Qw0AAOCSOCh2Hr99eN+De0ZfeXPLq1yT59I1HfZKU9MZLkFurukEAADALhw8Aozs\nM+Bqv0Nff/5LlmviFFtBXm6+Ex+Nuk5ioiRVtvZOfAAAwC042u4kesSsGZt73da3W95zTw7r\nWC8i8G8f8A4IqxBwGXumFF/2oZVzPpj55ferft22JzH1ZG6BPMr4BVeqVrNe86s69x50y01t\nqrnNer+LcGblXtmypnMAAADrc9DJtjzT7OxbsW/c3e2NIgY0eGrzlqcbOiHYX+TunHVHv3/N\n2JopSfLw8gsMCwvyU25WZlr8hqW7NiydM+nZp6598qMZ49uGOjtLCdu9W6GhYv0eAAC4fA6K\nXUjDngMHXqi3VWsYUqJ5ipK37vE+w2fEh7Ud8e9/Xde5/dVNo4L+jJ174uD2tUs/e+v5l794\nvGdvvw0rR9d2eqCSdOCA6tQxHQIAANiCg2JXtf/Ln/R3TZLzyv3mrck7Pa5+efmysVf884AG\n78DIRl2GNepyfbsRzbpOef71pQ++08VKe4ccOMACOwAAUDKK6EBbn7vSz6/qQ8tdH6Zoidu2\nnVC93tcV0erOEXTN3QNjdPT33xNdlatk5OervNtvJQMAACyhiGJXkJednZ2VW+D6MEULDAyU\nkhMTL7SHsKS81NR0yddqh3OdPm06AQAAsAsLPLUM63RNkzIpHzxw/4KE7PONyU38+sFxM9LU\noEvnSq7MdvmSklSliukQAADAFlyyU8llqnP/24/P6/7MO9fVmdesW+9rrmpSJ7pKWKC/t0f2\nyYyMtMTtv/6ybNGiNQezfRqNefuBeqbTXozcXG3ZoiFDTOcAAAC2cL5iV3AiOSEhwfHnfUIi\nq4R4l2SiIvhfPWHZqtoTHn1m8uKFH/y6sIgRflXb3vPUmy/c2SzQyVFK1ubNOn5cXbqYzgEA\nAGzhfMXu2PTBMdOL8XnX7GMnlWt080uLhkxI3rJmxar1W/enpB07npnr6RdQvnJ07UYt2nds\nXTP4gu9WuKdff1V4uK64wnQOAABgC+crdmVCqtWq5O/48zXCXPiygkfZyo063dSok+t+opPl\n57M7MQAAKDHnK3YhN0/fPqmjK5OURmlp8rLCKkcAAGAJFngr1sYyMlStmukQAADALih2AAAA\nNkGxAwAAsIkiVngF1+92443Hm4W7PgwAAAAuXRHFrtqA1z4b4PokpdHhw/JkzhQAAJQQaoVJ\ncXFq2dJ0CAAAYBcUO8PKljWdAAAA2AXFDgAAwCYodiYVFppOAAAAbIRiZ0x+vrZvV/nypnMA\nAAC7oNgZs3u3MjLUrp3pHAAAwC4odsbk5UlShQqmcwAAALug2AEAANgExQ4AAMAmKHYAAAA2\nQbEDAACwCYqdMSdPSpKHh+kcAADALih2xhw5In9/3ooFAAAlhmJnkqcnM3YAAKDEUOwAAABs\ngmIHAABgExQ7AAAAm6DYAQAA2ATFDgAAwCYodsacPm06AQAAsBeKnTFr16p+fdMhAACAjVDs\njElNVUSE6RAAAMBGKHbGbNqkZs1MhwAAADZCsTOmsFBBQaZDAAAAG6HYAQAA2ATFDgAAwCYo\ndgAAADZBsQMAALAJih0AAIBNUOwAAABsgmIHAABgExQ7AAAAm6DYAQAA2ATFDgAAwCYodgAA\nADZBsTPmwAHOigUAACWJYmdMXp4qVDAdAgAA2AjFDgAAwCYodgAAADZBsTOmoMB0AgAAYC8U\nOzPS05WRobAw0zkAAICNUOzMKCyUpIAA0zkAAICNUOzM2LpVkoKDTecAAAA2QrEzIzlZISGK\niTGdAwAA2AjFzozCQnnyvz0AAChRlAsz9u9X+fKmQwAAAHuh2JlRUMACOwAAUMIodgAAADZB\nsTMjO9t0AgAAYDsUOzOSkhQRYToEAACwF4qdGbm58vMzHQIAANgLxc6MbqD4fgAAIABJREFU\ngwdVqZLpEAAAwF4odsaULWs6AQAAsBeKHQAAgE1Q7AAAAGyCYgcAAGATFDsAAACboNgBAADY\nBMUOAADAJih2Zhw+LF9f0yEAAIC9UOzMOHWKI8UAAEAJo9iZkZiowEDTIQAAgL1Q7MzIzVVY\nmOkQAADAXih2AAAANkGxMyArS7m58vAwnQMAANgLxc6A9HTl5ioqynQOAADw/+3deUBU9frH\n8WcWdgQGEBBQQxHEJXGlzMClvKaS1a3MLU1bLE3Nrtbv5s213bJ7TS2Xq5ZtbrlVroXaYu6K\nqLmACVdUlE1BkGV+f+ACKirDMIf5+n7951lmPvM4zvk4c+aMWih2mtEzewAAYFWUCwAAAEVQ\n7DRw4YLWCQAAgIoodho4dUpEJChI6xwAAEAtFDsNZGeLiDg6ap0DAACohWKngbNnxc9PnJ21\nzgEAANRCsdMGX4kFAABWR78AAABQBMVOA6mp4uamdQgAAKAcip0G8vLEz0/rEAAAQDkUOwAA\nAEVQ7DSQnCyenlqHAAAAyqHYaaCoSLy9tQ4BAACUQ7HTQFGR1gkAAICK7KnYFWYmbo9bty5u\ne2JW4Q1W5yTv2rJlb4od/A5rcrL4+GgdAgAAKMdOil3ugc+HRtfxr9+6Q+fOHVrX97ur4+hl\nx69pdwemPXrvvb1nH9UmYUWYzeLhoXUIAACgHLsodinznry//7TNqY51WnXs1jWmiZ/87+cP\n/h797PIzWicDAACoPuyh2G39z5vfn3VoOnTt4aPbNqz6Pi4+cff8p0J0f81/5rkvU7UOBwAA\nUF3YQbE7sWVLsrg8OeHDBwOMJUvcIp7+fPn45o4Zy4YPX5qubToAAIDqwg6KXU5OjkjgXXc5\nll7o0PS1uf+MNJ5dNHLMhlytkgEAAFQndlDsagUF6SV5x460souNzV7/bHi4/q9PX3g97pw2\nyQAAAKoTOyh27g890snp4urXe05ceyzXXGqFU5sJ/x0Zrj869fFuEzadMZd7AwAAAHcEOyh2\nUnPAJ//pWjP95zf/FuLr36BZrznHL69xbfv2sund/dM3j+1QP+L5pWe1TAkAAKAxeyh2og97\nfuXeTZ+Neiq6rmP64QMppU6qc2j4/LLta997+j7fE3sOn9cuIgAAgOaMWge4TfqA+55//77n\n3xcR8zUfuhqCHxg9/4HRM9MO7U04kuUbrEk+AAAAzdlLsStFp7vhYqeaYa3bh9k4CwAAQPVh\nFx/FAgAA4Nbs8B27cvw0tv2EjRIyYO7cASG3v1dGRsaYMWMKCwtvss2BAwcqnQ4AAKDKqVPs\nTids3LhRzrTP0ToIAACANtQpdtH/t3LlAPEIq1uhvUwm07Rp026+zWeffbZ58+ZKRAMAALAF\ndYpdYMvugVpnAAAA0JC9FTtzfnpyYlJKWnZufrHR2d0UUDvkrkAPB61jAQAAaM9uil3uoeVT\n3p26YOXmg2cullmhc/Fv3K77U8+NHPZEoxoahQMAAKgG7KPYnVr5YkzPT/+8IGL0DGnepp6/\nt8nk4SwFeTkZJ1MSD+xbN2fMuvnTOn/ww3cjIl21DgsAAKANeyh2WYte6vPpn+4x/zf3/Ze6\ntQp2v/bae+YLx+Nm/d/g0V+90nVE08SZnZw1SVkBRUVaJwAAACqygwsU56z8cvk5j16frny7\nZ5vrW52I6FzqdBi2YPW77Yyp82auzLd9worat0/8/LQOAQAAlGMHxe7k//5XJCF3333zE+h0\nIZ061pOCxMQUG8WqhPR0iYjQOgQAAFCOHRS7WoGBOjmydWv6zTc7u3t3suj8/Hxtk6qSyvnB\nWwAAAMvZQbFz7fpUrEfOd0O6jvx619kb/vSXOWv/4tceHr7igsvfnuzuaet8AAAA1YM9fHnC\n56npCzYf7TljSu8WnwypF9mqWfhdgb41XB10+eezs9NTDu7auuvQ2Xxxqtf/i1lP19Q6LQAA\ngEbsodiJLih2+pa93We899GcZb9sW5e4rexqvVvwPU8NeGXM6CcbcyE7AABw57KLYici4h7a\nddSsrqNm5af9uXf/8dPpGZk5BXpnd++Au8IaR4SYHLXOBwAAoDW7KXaXOdUMbx0TrnUKAACA\n6scOvjwBAACA20GxAwAAUATFDgAAQBEUOwAAAEVQ7AAAABRBsQMAAFAExQ4AAEARFDsAAABF\nUOwAAAAUQbEDAABQBMUOAABAERQ7AAAARVDsAAAAFEGxAwAAUATFDgAAQBEUOwAAAEVQ7AAA\nABRBsQMAAFAExc7WTpyQwkLx8tI6BwAAUA7FztaKikRETCatcwAAAOVQ7GwtNVVExNVV6xwA\nAEA5FDtby8sTEfH31zoHAABQDsXO1lJTxc1NdDqtcwAAAOVQ7GwtP198fCh2AADA+ih2AAAA\niqDYAQAAKIJiBwAAoAiKHQAAgCIodgAAAIqg2AEAACiCYmdrublaJwAAAIqi2NnaqVNSu7bW\nIQAAgIoodhowGrVOAAAAVESxAwAAUATFDgAAQBEUOwAAAEVQ7AAAABRBsQMAAFAExQ4AAEAR\nFDsAAABFUOwAAAAUQbEDAABQBMUOAABAERQ7AAAARVDsAAAAFEGxAwAAUATFDgAAQBEUOwAA\nAEVQ7AAAABRBsQMAAFAExQ4AAEARFDtby8/XOgEAAFAUxc7WUlMlMFDrEAAAQEUUOw04OWmd\nAAAAqIhiBwAAoAiKHQAAgCIodgAAAIqg2AEAACiCYgcAAKAIih0AAIAiKHYAAACKoNgBAAAo\ngmIHAACgCIodAACAIih2AAAAiqDYAQAAKIJiBwAAoAiKHQAAgCIodgAAAIqg2AEAACiCYgcA\nAKAIih0AAIAiKHYAAACKoNgBAAAogmIHAACgCIodAACAIih2AAAAiqDYAQAAKIJiBwAAoAiK\nHQAAgCIodgAAAIqg2AEAACiCYgcAAKAIih0AAIAiKHYAAACKoNgBAAAowqh1gIow553ct+X3\nXQcSU9Kyc/OLjc7upoDa9SNaRLVuWNNJ63AAAAAas5dil5OwYMyIsbPXJ56/wUp9jdCO/Ua/\nNX5QG1/egQQAAHcsuyh2F7aOjYmZsCPP6FU/qlt02+b1/L1NJg9nKcjLyTiZkrh/68/rN0x/\nfsOy1XM3fdu/vl08JAAAAKuzhxaUNH3IpB3GNqPWLJnYOfiGH7mas3bPHPDwi0sHD57fZd0g\nf1sHBAAAqA7s4KPLs2tXby+uNXDyu+W0OhHReUa+sGBKT/e89Uu+z7ZpOAAAgGrDDopdVlaW\niK+//y2iuoWGBoikpaXZJhUAAEB1YwfFrnZYmLPsX/L13os326owfvkPSeIcGhpkq1wAAADV\nix0UO4duw4aEFu8c3zH6hY9X7Eg+X1R2dXHOifg1M4a27zhup7nusy92d9YmJQAAgNbs4csT\nDm3eWfPVmW6D5s98pcfMV/TOpsDagb41XB10+eezs9NTk0+dLxIR59AnZi6bHM317AAAwJ3K\nHoqdiEO9p+bFdxry7Wdzlq7b/Nv2g4cTUi6t0Tl61Y58ILrL4wMGP92proumKQEAADRlH8VO\nRMRYs3WfMa37jBGR4oKcrIzMnAK9s7vJ29PZDj5OBgAAqHr2U+xK0Tu4mfzcTFrHAAAAqFZ4\ntwsAAEARdvmO3Q1987iu1xJpPDZ+37gmt79XUlJSVFRUYWHhTbbJz88XEZ1OV9mIIiJiMFjl\nZgAAAK6lTrGzTN26dRcuXHjzYpeQkDBixAgHBwer3OPEiVa5GQAAgGupU+weX3Cu+zwxOLpW\naC+9Xt++ffubb+PqWrHbvLlatax4YwAAAFepU+yMzu7uWmcAAADQkF0VO3PeyX1bft91IDEl\nLTs3v9jo7G4KqF0/okVU64Y1uTAxAAC409lLsctJWDBmxNjZ6xPP32ClvkZox36j3xo/qI0v\n3/IFAAB3LLsodhe2jo2JmbAjz+hVP6pbdNvm9fy9TSYPZynIy8k4mZK4f+vP6zdMf37DstVz\nN33bv75dPCQAAACrs4cWlDR9yKQdxjaj1iyZ2Dn4hh+5mrN2zxzw8ItLBw+e32XdIH9bBwQA\nAKgO7OCjy7NrV28vrjVw8rvltDoR0XlGvrBgSk/3vPVLvs+2aTgAAIBqww6KXVZWloivv/8t\norqFhgaIpKWl2SYVAABAdWMHxa52WJiz7F/y9d6LN9uqMH75D0niHBoaZKtcAAAA1YsdFDuH\nbsOGhBbvHN8x+oWPV+xIPl9UdnVxzon4NTOGtu84bqe57rMvdnfWJiUAAIDW7OHLEw5t3lnz\n1Zlug+bPfKXHzFf0zqbA2oG+NVwddPnns7PTU5NPnS8SEefQJ2YumxzN9ewAAMCdyh6KnYhD\nvafmxXca8u1nc5au2/zb9oOHE1IurdE5etWOfCC6y+MDBj/dqa6LpikBAAA0ZR/FTkTEWLN1\nnzGt+4wRkeKCnKyMzJwCvbO7ydvT2Q4+TgYAAKh69lPsStE7uJn83ExaxwAAAKhWeLcLAABA\nERQ7AAAARVDsAAAAFEGxAwAAUATFDgAAQBEUOwAAAEVQ7AAAABRhl9exszFHR0cRcXLi18oA\nAMAlJfWgutGZzWatM9iBPXv2FBYWWuWmxowZk5ub+9xzz1nl1lBRs2bNEhHmrxXmry3mry3m\nr61Zs2a5urpOmjTJKrdmNBqbNWtmlZuyLt6xuy1W/MsLCAgQkb59+1rrBlEhGzZsEOavHeav\nLeavLeavrZL5t2zZUusgVYtz7AAAABRBsQMAAFAExQ4AAEARFDsAAABFUOwAAAAUQbEDAABQ\nBMUOAABAERQ7AAAARVDsAAAAFMEvT9ha9fxpuTsH89cW89cW89cW89fWHTJ/fivW1jIyMkTE\nZDJpHeQOxfy1xfy1xfy1xfy1dYfMn2IHAACgCM6xAwAAUATFDgAAQBEUOwAAAEVQ7AAAABRB\nsQMAAFAExQ4AAEARFDsAAABFUOwAAAAUQbEDAABQBMUOAABAERQ7AAAARVDsAAAAFEGxAwAA\nUIRh3LhxWmdQT0FWyqF9B5Kzde4mD6fb684W7ILyWDDMwqzkP/cfOJKSUeTq4+XCX0ClVOLJ\nnPvXtl93n3EMCqhhqKJwdwBL5l90/uTRhH2HU88bPH1qOOiqNqDiLJh//unD8fF//nXmorO3\ntytP/cozn07YtO3Ebb+QKHf8NcOqLh5eOLRdLeOl6ToHRw9fnHjR6rugPBYMM3PH9H4t/Bwu\n/4sweDZ+8qPfMm0TVzmVezLnxr0cqhPpNCOtCiMqzZL5XzyycGSnYMfL/wCcgjuNWXvaJmnV\nU/H5F5+Oezu2gfvlKq3zbPTER7+n2yiuunb8X5hIzO28kCh5/KXYWVXGmmdDDKLzvefZidNn\nffrOkPa1DKKrM3DNTWqCBbugPBUfZvGxWQ94iuh8W/Ud/e5Hk8cNiw1zFRH3TtOP2jC3Kir3\nZM79ZWSoXoRiZzFL5p+24pkQvehrRb/0/pz5M98f3inIIFKjxxdUu4qr+PyL9k9u4yLiVL/7\n8IlTPn73td4tvUSkRvS0I8U2zK2awpQvH6kpt1XsFD3+Uuysad/4ZjoxNh+7K//SgoKESa0M\nIg3f2GXFXVCeig+zeNOwYBHXDv8+VHB5Uc5vo8L1Ir7PrMkvZyeUo1JP5gtbRobrjUYjxc5i\nFsy/8I9RISKeD0xLLLy85OiUto4iTcf/WfWBFVPx+ResGmAS8Xj0yys1umD3uEiDiN/g9UVV\nH1g1efuXTn7z5V4d6tcoeQP01sVO1eMvxc6Kdo6uJ+LUfUHpsp869T4Rqf9aOU8TC3ZBeSwY\n5u7XQ0XcnlqWV3phyuR7RCT4H1uqMKuKKvNkzv/jtUZ6x5avj3yAYmcpC+ZfuLK/p0joP3eW\nbhFnVrzRs2eff2/lPaOKsWD+B8c1EZGun+eUWvbnW01FJGYq/wYqLG1GTJkTzW5Z7JQ9/qpw\nmmB1kbp5c6JIiw4dPEstDIiObiBydMuWM1baBeWxZJjHjyeLNGjSxKn0Qi+TSUTOnTtXhWEV\nVIkn88UdEwdOPtTsjTmvRnDiuKUsmf/ujRuzpG6PR5uXPhD4xE765psFw1rzDYoKsWT+np6e\nInLmzNmri4pOnDgt4hgQYKrStEryGbA8rcTOfzW7je3VPf5S7Kzn4J9/irg2aBBYZmndunVF\n5NixY1baBeWxZJidP01JS4t7tV7pZZlrVv8hIuHhYVUUVFEWP5kL9kwc+N7BhqNmv97MWP5W\nuAUL5n92+/Zjoo+MDEta9dYzXVpHhNaPiHro2bdXHs61QV7VWPL8D3j4yfudZOsHQ6fFZ5lF\npOjUxtdH/feU+PTq24X/4lSYztnTt4TJ9XZeStQ9/lLsrMackZEl4u3tXXaxh8lkEMnOzrbO\nLiiPRcN0quHr6+vpfPW9idz4qX2GLEoXj9ghfetUZVzlWPpkLtzzzsD39oWMnP1mC8fytsGt\nWTL/tLQ0Eff0hbHNY99cuCfHvaZn/qF1c954uHnb1zdm2iK0Qix7/tcb8tXCV+/NXzE0spZ/\n/bC6vnXaT97u3undVf/p7l71ke90Ch9/KXZWk5eTUyTi4OBQdrHOyclBxGw2W2cXlKfSwyxK\njZv82N1thv1w0qXx4G9mP12zioIqyrL5F+57f+Bbu+oMnTn+Hueqz6gyS+afmZkpkr155cF7\n3v8j+cT+bb/vTDyxb0Z3n5w97w0Y/0eRLWIrw8Ln/7HNK9YfzBC9i6e3ycvkXcNJ5Mz2r+es\nSWL6VU7h4y/FzmqcXVx0Nzgzy3zhQr6Ih4eHdXZBeSozTHP69hkDW0V0GPXdUcfIgbP/2DLj\nIb+qzKoiS+ZfdPCDQRN2Bjw3860YF1tkVJkl8y85eBk6TPx8VCvvkretXRoO/mhEpMixpUt3\nVnVkpVgy/+JdY7v3m7PH2HXK1uQTB7dv3X00Nennf7Ur2jO7/9OfHLNB6Dubwsdfip3V6IKC\naolknTlTWGbxydRUs0idOjf6XM+CXVAei4d5bvuUrk3vfWnubmna+6O4A9vmDGrKxyAVZ8H8\nT897ZfxWXds+XfXb40r88me6iGQc+jUuLm5ncp5NgivCkud/ybn7IVFRZf4b0yD6/loiKSkp\nVRdWQZbM//fP/3uwSKL/9d8RLU0lvdqhVvsJM19tIhd++XoZ869iCh9/KXbW07hZM4MU7Nix\nt/TC4vj4/SJBrVr5W2kXlMeiYRYfmdHjwZGrT/o8OH7d/p1fvhITyPn7Fqr4/NNTU/Ml77d3\nHulwWezkbSKyc8ojHTp0eOnbk7YJr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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "library(ROCR)\n", "ROCR.pred <- prediction(prob.true(x), y)\n", "ROCR.perf <- performance(ROCR.pred, 'tpr', 'fpr')\n", "plot(ROCR.perf, col = 'blue')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The ROCR library has also a convenient function to compute the area under the\n", "ROC curve (AUC)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "
    \n", "\t
  1. 0.940316870450693
  2. \n", "
\n" ], "text/latex": [ "\\begin{enumerate}\n", "\\item 0.940316870450693\n", "\\end{enumerate}\n" ], "text/markdown": [ "1. 0.940316870450693\n", "\n", "\n" ], "text/plain": [ "[[1]]\n", "[1] 0.9403169\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "performance(ROCR.pred, 'auc')@y.values" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "If you want to know more about the `@` run `?\"@\"`. If you want to find all slot\n", "names use `names(attributes(performance(ROCR.pred, 'auc')))`.\n", "\n", "Finally, let us plot the ROC and compute the AUC for artificial data sets with\n", "different Bayes error rate. We will use the following densities to generate the\n", "data" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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XSee+65vXywy+VSKBQZGRnxqyfqYdufbyj4d5lMLakBj+AOsnr+Tk2pvnTdOGUG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\nXv8n7oqvJsX1LkmxOcT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2wzBmkw6wr9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xxpVShWV0SZAPxCsSrJq8y8yzsjV5qaoM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\n8idJEUIRYvZHLcGj+xl+9t/n/aP73xfHcZzFYul9VWq1uis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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "for(i in seq(-1, 2, length.out = 10)) {\n", " f <- function(x) prob.true(x, 10^i)\n", " curve(f, from = 0, to = 1, add = i != -1, col = 3*(i + 1), ylim = c(0, 1), ylab = \"probability of class label TRUE\")\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Which of these data generating functions will lead to the lowest/highest Bayes\n", "error rate?\n", "Now take a piece of paper and draw a prediction for the ROC curve for data\n", "generated with the function shown in black and the function shown in red.\n", "For which one of those two do you expect to get the higher AUC?\n", "\n", "Once you have made your predictions, run the following cell." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AUC(b = 0.1 ) = 0.515228205372214 \n", "AUC(b = 0.215443469003188 ) = 0.52438619538806 \n", "AUC(b = 0.464158883361278 ) = 0.525077028620369 \n", "AUC(b = 1 ) = 0.584017681768176 \n", "AUC(b = 2.15443469003188 ) = 0.673596027080295 \n", "AUC(b = 4.64158883361278 ) = 0.813775139997101 \n", "AUC(b = 10 ) = 0.935383506348203 \n", "AUC(b = 21.5443469003188 ) = 0.984033974241319 \n", "AUC(b = 46.4158883361278 ) = 0.996698438811437 \n", "AUC(b = 100 ) = 0.999346926144651 \n" ] }, { "data": { "image/png": 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uOYl2yZ5KDs8DZLPGI5H/isEyEkN4r814HIrhBBE46FybYZroy7CmxnuEgbRfyw\noRYAos6raSJGlYrSqmpBrJfLSpWitmuajDFCyE6SI1lmKEObCSKTolIoaoqJRQhZCCJRNt2K\nFVHFtX61wqe+tp+v8avXjbYOT2aKXHTp6dcrObmNXZ+/3/bqmckLj051CCH/e5+xuZnpv/kZ\ngrT9feCKGxt1dXU7d+5cs2bNyQ/TNO2zzz4jCGLcuHED07A+0Hmt6602YV/Y93Y70rBlvCPt\n1tz0O/Nhe6VEpPnV9r/VBdZ0ieU8m8PRqQxBEbaZSblPDDOPssHuCyDeqBi3appf17+W5EOK\n8ikv6AhRCGXTtJ0kimj6XAs3nGFmcKbBUGEkWhQdRxTsjejb2+TmkOYT9M1NUjuvWRii1E0/\nv9A9LTvK5YTqI9X1QrVf6f7U8/6Z7vlXZd945Eeq1xfeWCZ8cyDt1zdCqjsVEOxio76+HiE0\nffr0kx9WW1sriuKSJUus1jhdZNDxREP7I3WIIKzTnem356XdkQ8beSUWrGH+K7+wPyw1iIFP\nvVKDSJrJ1J9mZz841D7TBekcxINWVdsry9263qppTaoW1HWEkF/Xw7ru1XQRY4SQkyQLafrv\nyUmjWNZFEhDj+qApqFV3q41B9dX9kfqAihCy0ERpMmNnictHWObmm4YlM2Q/9Gyu71z1ZuuL\nNsqRbso8I2nOZVk/7lkqIdc2BT5ay2/9hmBox3lzLJPHRP+5jQiCXWz84x//GDVqlM12slJt\nmqbt3r371OuhDCiMPM81db/Xwe8MZvwyP+3/cukUqAebSJQOObDKG/i8K7y5WwuoTDprHmVL\nWppum5VkneSg+lp0CoAokjA+KCv/CYW/FCUCIQtJDKEZF0VONZkohAgC2QnSQhLDGSadomz9\nkTgGjcagtrZe/NfXYUnDSRw5MoV5dI7TwZLFSXR//16bxPo3Wl6Yk3LulVk3kMThOC7XNXuf\nfEVpbmcy01J+frV1xgTYK+zUwcd3bKxfv/6RRx45+THt7e2RSGTSpEkD06RTgSVdOBD2/rs5\nsLpL7ZTdV2Zm/rbQsQBWRSQALazxX/nDW/1Yw2qH7P/YixXdNisp675i5zkpbH5i17sGxrBX\nlndLyhpBEDEWMG5RNQnjDIr6fZJzscXMwTS4qOIV3BLSllcKn1YLrWHNRBEXDDXfNsmWNYCj\nLp97V3zU/la6KeuijCuPpDqEUGjtl1iS0++91Txu+IA1xjAg2MVAdXU1z/Pjx4UUIoAAACAA\nSURBVI8/+WGhUIhlWYslLpb/YEkPfdHdcFu50iKxBeb0X+TbpjutU5yxbhc4GdUr82WB4Dpf\nZHeQ3xFECFnG2akkBiGU8euClBuyYV0LiKFGVd0oSD3LGgSMP4lEmlQtjaJmcaYxLIsQcpDE\nRBObOugLxUVdRMHP7Q6/so8Py9jOEteMsp6RbZqYyfTLOOsJCFpkT3DHu60vn59+6blpF5nI\nw/eW/JZvImW7hV0H7QtnQarrG/hYj4ENGza4XK4JEyac5Bifz7dv3760tLQBa9VJ8DuCtVfs\nVdolx4LkoSvGc6VWBHfO8Y3fFvCv8vqXe6Q6wXaGyzLRmfHrQss4O5MJ9TxBzAgYKxjXq+qT\ngVCLqtWrqoUgCpnDl6GZHDfPzM2AkrPRpuqo0qcoOlpbJ9b41cagVutXMUbXj7ZcOdKabaeo\nAf88/9K37j9NTyGEJrvOWJJ+KUkczu6htVt8/3nPNKzIedF8x/lnD3SzjAKCXQw0NDSUlpae\nZLPXSCTy5Zdfsix7xhlnDGTDeuV7q73l/mo2jytdP4nNgwG7eCc3i6EvuhtuPsiVWLmRtuIP\nx3FD46LTFwxOXZq+MiK8HArzGPO6riGEEBpvYi+xWSab2BEMA3VG+lWVT717g3+/V0EIWRhi\nYSG3qJjLd1DTsk0pA142XNAiy5qebBOb26TmCc6pS9Ivz+HySYLEmhb4cI1U3SB8vd8+f2by\nzy6D4sM/BAS7GNi7d++wYcNOckBZWVkoFJo7d+5Jwt/AaLqzovOlFteS1NzHS+lUmLsaX7Ck\n64KOEPJ/6o18HQxu8EnVkZ4fuS5IK3x5FPEDdmkEoA8qFaVcVryaLiP8eURs1dSwjk0EcbHV\nMs/MMQRhIQgCoSKGhglz/W1Xh/LglsBuj5JsJt+6ILnUTZsogotd7ckvfetWeT7sVroWpV1c\nbCktsY2gCQYhhCW5/c9PS1X11hkTU++83jozjqaVJygIdjEgCEJu7gkL9Muy3NHRMWbMmIyM\njIFs1bHNaBDrf7o/XBbIfbw09YYcGHuNCzoObepu+0udVC8obdLRP7HPTkq6KM023UWnsmw+\nR7ujsLEPACfi03VexyFdb1DVVk2rkBUFIb+ubxcljiDyGZpEaBhL38zZ0ihqGMtYIcYNoJCM\nf7vRv7pWnJDBvnCue0Y2G8M8hxGOaPynHe+t8X48xTXzpvxf5puLjz4g8vV+6VBt2m9uskwe\nHatGGgwEu7hTW1urKMqQIUNi1QC5Qez+yOP9dxNpokpWT7SdEX/FVgYfLaQqLVLNpXukWsE2\nzZl5TyGbyxE0QbkYhBBpJbmSOK10CBIaRqhRVVtVrVvXt0tStaI2q1qHph05gCOILJpKo6g8\nmkoi6atSrHPNHIS4WGkJaRsapXfKI80h7Z/zXAuLuIFcD3FsY8TGtd5PGoTaBqGGQMQ1OTef\nlbzw2IMwDq3dwo0uhVQXRRDsYkAQhBP9SNf1srKy3NzcmGwgxm8LdL7S4nu3gzSRznNSMn9f\nZCqK933MjE1uFjtfbOn+oENuFrGCSY4sfm+sY14yjLGC/tamaf/wB7+SZK+mEQjZSTKDomZx\npsUWKpumrQSRRlE2kkiCOsDxQdHxS3v5p3aGMUJj0pj3L0oudsXs+q5j7aXmf+30b01lM4qt\nJZdmXZfN5TvoY6soRLbv7fzX6zofSbv7hpi006gg2MVAWVnZdddd1+uPampqEEInXzDbT7rf\n66i/8YB5lC3n4aHJV2WSFigxEANSnSDsC3Uv90i1glQT0fwqaaGSr8m0z06yjLWz+WYYEwf9\np0pRV/CRSkXx6foBWTERxJ1O+0iWHQFjqXFM1vCHlcLKarGsTbqk1HLPdIedjeWL9UrzM9u6\nN2lYuzL7himumRbq2MEEpc3b/cqHUnWDFghZJo1yXbaYLciJSVONCoJdDGCMi4qKjv++LMt7\n9uxJT08f+K0mpOpI452HXBekFbw4EnqDBpjOa1K9oHYpzb+qFA6EEUKWiQ7H2W7u57lMpsk6\nyUkO+OI1MHh4NW05L3zARxpVFSFUSNNTOdMokrzFYZ/BmcyQ5+KYhtHaOvGd8shXLfLsXNPL\ni90zsmNcLGaTb+0XXWuWZl49PeksN5PS6zHBT9aJ5dWupeeYJ41istIHuIWDAQS7ONLS0hIK\nhebMmTPAz6t45JrL91J2OvuBYkh1A0Npl4R94cjuUGi9r2c3CISQZZx9yIrx9pkuwgRJDvQj\njFCNoh5SlH2yvJwXQrp+qc1yr9mZTJLDWQbefPGv0qf+ZqO/MaCFFX14MvPioqSZOTGOdCpW\nN3atfq/11bkpixenXdLrMVjTOv/xcuTr/c4L5zuWzB3gFg4eEOziSE1NTWZmZnLywO7QpeOm\nX1ZoIXXopxPYAphR148iu0OdL7WoXiXwmRcrGCFkGmIxj7IVvjLKPNZOJzFU7ObEgMEgqOvd\nut6qas8Hw2WSxBFELk1dbbP+xG6DjVYThazhNw9GntoZtrHEH2c5RqQwMZxLd0QVX76s8Z8e\nuX1uyuIrsn7S6zFaINTxwFNKR6frknPt584e4BYOKrF/Qww2gUBA13XquE1yNE1rbW2dNm3a\nALen45+NgZXeorfGQBnb/uN5pqnzhWaxKmIqNLsuTMt+aKhtmss0xAw7eoGB4dG0raJ0f3eg\nZ/+uFIp8MTV5GmeCibSJQtFxRMGra8Xnd/NeXls0xHzvdLsjPrr29wa/fqr+oRLryJ8X/jaX\nK+j1GM0fbLvn71oglH7vrdzIoQPbwEEHrisDLRAIYIyPr2PX1NSEMc7Ozh6wlqg+pfaKveEt\n/tSbcpzn9D4ZAvSZWMH7P/KEtwWk6ohUJ6TelJP/7AjrNNhdFwyQfbKyT5YbVe0rUapUFITQ\nFTbr7U67hSBYmDmXUFbWCH/YFAxIOoHQOUXcL89NKoqDXjqEUBVf/nbrf+oiVaPtE+4ovPfI\nzmDHCK3b6nvxPcppy3r0N0xOLOuzDhJx8eYYVCKRCEKI+O4HayQS+eabb5xOp9U6QNXIIntC\ntVft0/xK0ZtjnOcM7OCvsWEU2tQdWN3pebqRyTI5F6ZYxtutU13OBcmwoBUMjJCuPxcMvxIK\nuykqh6amcuxvXY5Chs44bqAAxK0OXnunXFhZI3gjekDSx6UxD8xyO01kriMuXsQqvnxFx9vl\nob35luJ7hvx1qHV478dhHFq7JbRmM5uXmXbPLZTLPrDNHKQg2A00j8eDEMrJ+XZ1N8Z4+/bt\nkiQtWLBgABqAJb364t2hL7q5oZbC5eOtkx0D8KSDBJb0Q7N3CAfDpgJz2v/l5Tw0FMIc6G8d\nmiZh3KpqLZrWrekRjN/j+ZCO/5DkvNRmhTdgwtntUV7fz29olDBGFww1T8pkM63khIy42NGx\nS/ZWRw593PFOm9icby6+rfCeMfZJJNH7iLBUWdfxp6d1SbZMHOW68nxIdQMGgl1s0PS3v3m/\n319XVzd9+vQBWDYh7A833VUR3uIveHGk64I0qKMRLd3vdXifb5JbJaVDLv3vJOtUGHIF/aVL\n058Ohto1bbckyxhHMO75voUgRrMsSaD5ZvMdTrsTSgcnFIzQ+gbxtf2RzU3SkCT6F5Ptc/JM\n2fa46J/r8W7ry2s6P8YYj3VMui7n1hLriJMcLFXWeZ94ic5MTfn51VCmboBBsBto+H+fwkdI\nkoQQKikp6ffn1nHdNfsIEzn00/H2s9z9/nSDQGRXiP860PlCi3Ag7L40w3leqvOcFG4Y7O4F\noknEeJsoVSpqo6oekJUqRUmmqEUW82zOlESSWTRVQNMczJxLQAc7lb0epdavflojhmRd0nCh\nk/7HPNf5Q+KrQIGgRbZ2b/jcu2Jp5jVzUxaZSK6XgzAW9hwS9pRLlfVyXROWFSYnI+WWqyDV\nDTwIdgOtqanJ5XIdPceO53mTyUT29+21jmuv2idWRYZvm2oeZevf5xoEgmu6vC82B9d00ckM\nN8xasmaibQZsqguiZosoHZSVRlVt1bR9shLR9UKGzqbps83crU77DM4EW0EkLh2jlrD2yj7+\n9f0RF0c4WPLiEvOIFGZUKpMXH1PojsAIf9z+zscd7xAEOcM959y0i4je5pdovkDHX56RG1rY\nojw2N9Nxziw6NZktyiVYZuDbDCDYDTRN05xO59HBLhAIWCz9Xmqk9S91/k+8OY+WQKr7IYLr\nfMG1Xd0fdCgdsmOeO/+5EUlL06GqM4iWbaL0VpjfryitqlZA0/kMXcowc83cPDOXBksfEp+q\no5U1wl+/CnojOkcTv5xi+/EYKxOvRQSbxYZ1nSs3da29JPPaM9xnH7/Z6xGBFWtVT1fmQ3eZ\nSgoHsoWgVxDsYi8UCvX3HmKRb4Ltj9al/V9e6o3QK95Hnqcauz/yRHYGuVJryk+ze5a7xrpR\nwCBCut6gak8HQ18IYgZF/dRhS6OoBebeBrxAApI03BTU9niUd8sjuz3yOUXmm8ZZM21UEheP\n8yBVrL7Q+ESDUOuR2syU5Se5t53hPvskx4fWbgmu+iLpqiWQ6uIEBLvYa2trGzZsWD+dXG4S\nA6s72x+uYzJNsGNY3wgHwoFVna1/qnFfkZl2S27SJbC5IYia1RHhiUDIq2kCxikU+VyK+0zI\nc0bhiehvHuA7eP2TakFQsYsji1z0m0uSJ8bHEtfj8Vp4Rftbh8IHPHLruWkXj7KPL7aUfv+j\nNu+wThvnOB+2CIsXEOxiTxCE9PR+yQq+d9vrf3KAtFKuxam5T5TCDqR9oPqU6ot3Ix0lX52Z\n/8wIKF8CfiAV482itFuWqxVVwHi3JC+0mM/iTCUsk0ZRMHPOGCp86qYm6ckdIRdHFrroOybZ\n5+SbCl00FZcvb1D17/Rv3R3cURupJBAxO3n+WMeNJdaR3/tAzefnt34jltek/+4WgoLrS7yA\nYBdjVVVVCCGGifYMU4zaHq5rf7TOeV5q4UujoKzJ6ZKbRC2oiof4lnurNb86/KuppqL4WqcG\nEouG0AZB/EIQd0hyk6oOZ5kMipphMi00c0utFhrynFFsapL+vTtc1ipzNHHJMMtvptk5Oq5f\n3Bq+4sWmfwaU7qHW4UszrxltH5/CnlJHg//dVf73PiNo2j5vhnn8yUqfgAEGwS7Gdu/ePWTI\nkJSUKO/oJRwIt/2lNv3O/Kz7Yfj19HS/3+F7uz2wuhMhRLCkeaS15L8T2RwYHQN9cUBWmlT1\nS1FaI4ghXR/NMvMt3DwzN5aN08E40Aeqjl7ex6+tE1vDWmtYm5bNPn+Oe06+Kc4/eWv4infb\nXq7iy4dah99a8OsTbfPaK2F3efCT9c6L5rt+tIhgIEjEF3g9YgxjnJWVFfXTdr3WSqey2X8q\nRvG63ireCPvDoQ2+wKrO0OZu5zkpeU8Nc8xxs3kc/ALB6VIw3ibJZaK0S5a/kWQXSbpI8ka7\nbQZnGs4y0HluGIqOH98eLmuVavyqrKFLh5kvKDGXuukJGWw8f2pghPcEd27sWr0v+E0ml3N7\n4b3jHJNP6wzC7vKOB/9lnjgKUl18gpdkoPn9fqqfyxZ0vdbm+VdT+i/zIZScCn5n0PN0Y/f7\nHaZCMzfCOnTlBPuZSbFuFEhIe2V5ZUTYLsqVilLI0FNMpjudjskm6JwzIIzQHzYFP6iIXD3S\netVI6/h0psiVANdTjPAnHe9+1P7WSPu4m/Pvnuw643TPIOyt8D62jM3LSv/NzxDsbhKXEuCN\naDB+vz83N7fna13XVVWN7vmFg+HGOw4l/Sg9+09Dontmg+l+vyO8LcBvD0R2Bblh1vznRyRf\nmQlrI0AfCBh/yEc+4COVspLP0ONZ9iG3aziUZjWooKRvb5M/qBDW1ImPznEtLU2Y2bdBNfB+\n26tf+tZNTzrzxrxfnO7DlVaPuL8ytHoTW5Sbds/NkOriFgS7WPJ6vZIkpaamRvGcTbcf4oZZ\nC56Dqay9wwr2vdPe/vd6qVawTnZYxtqz/lBkm5kE60tA39Qo6k+9XV5NO8divtPpOIMzQR1h\n4wlKeo1f29oifVIt1PpVhNGoVOaZhUkLCxNm9m2X7L2/8k4zZbk255azkhee7sPFg1WeR15A\nmsYOLXBfcwHJmfqjkSAqINgNNK/Xy/5v3rQkSRRFORyOaJ3c93Z7eFtg6KfjobJJr7SgWnv5\n3vC2gOv81ILnRlinnbCQOgDfS8D4v4J4r8/vJsnPMtPyaPg4NaCIih8rC71bHomo2EITcwu4\nuybbp2ebbHE9j+5Y7VLLI9W/N5Hcg6VP9b7T64lgLHxzwPfKcqW1wzymNOWO6yknFGaPd/BJ\nNNB4ns/Ozu752uv1Op1Ryxb+jz31Nxywz3Hbz3JH65xGonjkmqW7pWqh8OVRriXR7CUFg83j\ngeALwXDP11farL9xOVioV2Is37TL33Qo/60XD3QqkobvnGS/brTVmpgVBnYFyl5tfs5G2387\n5KHTSnX81m+CK/4r1TRap49PvulybuTQ/mskiCIIdrEkCILNFp2dWzW/2nBLuf3MpKGfjI/K\nCY2n6RcVUq0wdOV4y4SodZGCwcajaR/wkWXB8M8ctlkcl0VRWTQMvRpKhU99+KvgpiYp205N\nzGAvKjGfnc+lWhJyDORAaPfazk/2Br+e6pp1dc5NVuo0LjeRHfu8T7xkHjc88+FfmYbk918j\nQdRBsIslSZIsFssPP49YzlfM34k0XPjKqB9+NuMJru3q+EdDaFN30RujIdWBvtkqSg90BxpV\nNYkkL7VZ73Q6ErL3BvQmKOlfNEkfVgjlXYo3og9Jov85z3XekIRZFXG8DV2rt3V/UcWXF1qG\n3pR/11TXrFN/LJZk/7urQmu3cKNK0mGRRAKCYBczoVCopaVl8uTTKyB0PF3Qay7fy6SyJWsm\n0ilQWOE7IrtDbQ/XBVd32mcnFb0+2rUkLdYtAolEwbhd078UxU8jwj5Zmc2ZHnS7img6GXZP\nMorqbvWS5Z0hGSOE5hVwPx1jG5fODEtm7Ak1he5oXbL3o463tvjWT3HN7EONOqxp7Q88qTR3\n2Bec4bxwAaS6RATBLmY6OzsJgigpKfmB5+l4rF7tkIZ9NZVOhVT3HWIFX71kF53KFrw40nVB\nGuzAAU6RgHGtono07a/+QJOqWQhivsV8qdVyntUCw67GgBF6+2Dko0phZ7ucbqWeXegqcFKZ\ntsR+eRUsl3VvfqPlBR3rN+TdOSPprNM9g1zb6P3nK0qrJ/33t5rHDu+HNoKBAMEuZniet9ls\nP7BYsc5rXW+0pdyYYypM4FGD/iBW8PU/OUC5mWFfToFSJuBUtKraF6J4UFY2i1KHpiGERrDM\n2+lJwxkG1kYYSbeo3785sKpGPLeYW7bIPSObZamEf329csdLTU9V84eG28bcWvDr01v6ihBC\nKFK2x/vEf9iCnOwn72MyYXlZAoNgFzOBQMBqtf6gU+i46e4K1SsnX50ZpUYZR8fjDVpILX53\nLKQ6cHLduv6VKL0cCpcrqpUghjHMEqt5qdWSTFI22LvFQFQdtYW1slbp2V28J6I9Osd1ceLU\nFj65g+G9zzX8nSGYu4sfKLGOPN2HS1X1vmXvSXVNtpmTkm+9moCZBgkOgl3MiKL4AyvYBTd2\nd73WVvjaaK70hwVEA9EjWvf7HW0P1cnNYtYDxdww+M2AE+rU9JdC4TfDvITx2WbuJod9Gmey\nQuecEa2uFR/eFmwKaixFnJ1vev6cpCFJCX/5C6uhvaGdH7S93q10jbKP/1neL2z06V1TVE+X\n7+UPItv30ukpKbdeZZ02HlKdAST8OztxeTye4cP7PokBa7jpjkP22UlJF8GCAIR03PlSq+/d\ndqk6onTI7kszUn+WY5kAhTRB714L8asiwl5Z5ghiqdVyu9PugEniRiSo+KNKYWuL9FmNeHY+\n9/T8pBw75eIS/rVuEGp2B3ds697UJXtLbSN/knvbMNtoijiNiT1Y04IrN0bK9qgdnal3Xm+d\nOan/WgsGGAS7mNE0ze3ueyXhwMpOqU4o/mBsFJuUoAKrO2sv34sI5L4sw3VhmnNBsqk4CkVk\ngPEIGG8RpZURYb0gzuBM/0hxz+ZMJuiiMyK/pN+zMbCzXZY1PDmTfSShNnU9OUkXn65/WNal\n0fYJN+TeUWwtPd0z6KLkfWyZsLvcMmm0+7qLTCWF/dFOECsQ7GKD53lFUTiur/sMYuR5pskx\n182VDPahRi2seZ9p4oZbi94YYyoyyAc3iDqvpr0S4t8M8zLGM83c7U77UqvFBb10BrWrQ/nr\nV8GabvWWCbaLS8xuA020bZOan6r7a5fs/e2Qv/RhOh1CCEty8433YlnJeOB2bgRsJmFAEOxi\nQxRFhJDL5erbw/2fesNb/UM/HeybTIhVkbpr9snNYvE7YyHVgV7tleVVEfEjPkIhdKXN+mO7\nDarQGVinoJe1yn/eEnBz5FMLXDOyjbNXvYqVKr782Ya/m0nzX4Y9nWnK6ctZdL3r329jTct+\n6j46LTnabQRxAYJdLBF9HQMKb/Wbh1vts5Oi255EoYt6x2P1/hVeoTzM5puHrhhvmQj7SYBe\nbBWlWzp9Qxh6qdVyk8MGE+kMbHub/OTO0F6PImp4Ugb7rwVJSYk/l66HjrXt/i2rPB82i/XZ\nXN6viv/soPu4ybjv1eXhTTtSbr0KUp2BQbCLDZ7nUV+DHVax/yNP8lWDt8RJ3fX7Qxt8yddk\n5Twy1DbDRZgM8vENoqJT02tVpUZRDynK6og4hmWeS02Gta7Gts+r3PlfP0cTD8xyzsk3uYzy\nmRBWgys9H+wMbPXJnaMdE36c+/MCyxAC9fHNLFXVh9dvcy1daJszLbrtBHEFgl1sVFRUZGZm\n0nRffv+epxvVLsV9eUbUWxXnsIq73+/wf+wNrOosfnuMc1FKrFsE4ssaQfyEj6wTRIwQRxDT\nONNii/kulwNSnfFghA54lW2t8heNUnW34pfw8GT60TkuAxQxQQjpWNsR2Pq556NWqclEcrPc\n88c6Jg21/qCtILCseB9bxhbmOM6fG612gvhkhL+BRBQOh4cOPe1Zq1pQbbzjkH+FN/22PNOQ\nwbXwM7InVPOjPUqbZD/TXfT6KEh1oIeE8T5ZeZ+PlMtKpaKcaeb+6nadbebsMOpqXN2i/rey\n0DvlEQtDzMwx/XyivdBJjU1jbQm7wevR9od2vdL8jE/uHOuYtCB1yUj7ePtpVqc7ni6I3a8u\n1wUx+ZYrSStMRzY4CHaxoWlaH7rr2h+uC67uyvpDUerP+jRtNmHVXbe/+8MO6yTHkA/HmUfZ\nYt0cEBc0hL4QxAe7A22aVsowk03sA27nOBZ2TDYsTUdlbdInVeLySsFEo7+e5bx0mKHubzHC\nb7S8sL5z1TjHlNsL7s01F0TltKF1W7ueewthnHTl+UwG7BVmfBDsYkDTtFAo5HSe5uxXHfve\n70j/ZX76L/L7p13xB6Pgui7PM03BNV15Tw1LviaLoI1wRw5+CJ+u8zrGCL8R5l8N8VNMphdS\nk4sZ+CgzMg2jDyoibx2M7PMoRS76gVmOc4s4h1Em0iGEdKxX8Ptfanq6U/b8OPf/ZrnnRevM\nWNUC76+2nz3ddfliKqmPSy5AYoFPw5gxm0+vP7zuuv1Kq+Q8Z1AMQWIVixV8633Vgc+7rFOd\nxe+PHST/cXASMsYPdAdW8BENIYQQSxD3JTmvsA32Uo7GFpbxK/v41w7w3aI+v4C7ZbxtQWFf\ny3/GJYzwofC+5e1vVvOHcriCe4c80oeCwyeihyOtv35E9fqsZ06GVDd4QLBLALqody5r6V7u\nyXt6uHn0oBiIbPx5edcbbUyGachH4xzzYFn+YBfQ9ReC4dfDPIHQvUnOMzgTgQg3RcKqCAPD\nCL28l39hD+8T9MuGm68bbS1yGe2Ctbz9zR3+LR1SazaXd3fRAyPsUd1JCGPPI8/rvJD1+O/Y\nvKxonhnEN6P9nRiSsDvU/JvKpIvSUq41fokTXdTrrt0X+Kwz6/7i9DvzCQau3INaSNc/i4iP\nB4ISxjfYbZfaLGnUaWyICRJUhU+9f3NgZ5t85UjLdaOtxYaLdD6lc5Xng01d/x3vnHJj3p2F\nlijvAKGLkufBZ8TKuvR7b4VUN9gY7a/FkLSgihAqeHkUIg2ecrSgWn/jgcCqzpxHS9JuzY11\nc0CM7ZeVxwPBMlE6z2q+x+WEHcAGgw5e+83GwH6vkmwm/7UwaaGxBl57YIT/3fBEh9z6o6xr\nZybNNVNRXgKitHs7n35Nrm5Ive1a89hh0T05iH8Q7GIAY3xaxwsHwqYhFoIyeKqLfBNs/1t9\naGN33tPDU66HW8zBq0vTVwvCekHcJclZNLUsNXkaZ5yNocBJvH8ocu+mAEsSv5pmXzLE7DLK\n1hFHa5Oa32pZVh0pv3fII1HuqNP10PqvwhvLpEO1dFpy+h9v54YVR/P8IEFAsIsBVVXR6Sye\n4L8OsjkGvG09QumQW+6p8n/sMQ2xZD84BFLdYLZOEO/o9FEEscDM3el0XG6zsDCRzuiCkv7Y\n9tC6Bqk9rF02wnLPNIcxKtIdL6yGPmp/qy5S9YvC+6I+/Br679auF9+1zZ7sOPcsy+TRBMtE\n9/wgUUCwiwFN0wiCYJhT+qvDGua3B9Jvy+vvVsWK2qVUnfuNLmhZfxqScl0WaYUZVIORiPF2\nSXouGN4tyQss5j+4nMmUAXtrwDHCMn60LLi8QmBp4sejrTNzTePSDBtHeC18X+Udgha5NOv6\nkfZx0T256unyLXvPsfgs93UXR/fMIOFAsIsBXdfNZjN5ahOGwlv9SqtkmWzYTe6rL9yleKTS\ndZO4UqhbMRhpCFXKyt2+7lpFHcuyT6W455qN3D8Nekgafnkv/2mN2BrWrhppuWGcLcVs5Ci/\nvP3Nz70rCET8ufTJFDYt6ucPrvqCtJqTrr4w6mcGCQeCXQzouk6c8uiS9/lmbqjFNs3Vr02K\nlfBWv1gZyX96OKS6weagrGyXpHJZqVTUQ4qSQ1MrM9KKoM7wIKBh9J+9vqrlnQAAIABJREFU\n/FsHI15em5Nv+uuZzlGphu2lQwh91b3xw/Y3umTv4rRLFqVdHPWlEljTAx+sDq7c4Fq6kIB+\nbgDBLiZ0XbdaTynHiFURYW/IfVlGfzdp4IU2dXc80RDe6jcVme1nu2PdHDBwGlX1yUBoZURI\npsjxLDvexP4hyTnWxMIY/GDQFtZ+uspX1a1eP9o6r4CbmmXkLeAULH/S8d7nnhWjHRN+XvDb\nfHMRgaI8d1Bt7/Q++bJc25R01RLnhfOje3KQoCDYxbWWP1Trkm6wCr1Ki9Txz4au19vMY+wZ\ndxWk3pJD2eF9aHwqxrWqupwXXg6FLQTxkNt1kdVQG32C7xWU9LvW+4MyXrbIPTvX4Cud6yJV\nrzU/1yG3XZhxxYLUJRQR/TsXfvOOrhffpZKcmQ//ii0YXBuIg5OAC2r80kJqeKMv8/5i61SD\nbAWj81rjHYd877TTSYz70oyMewqZdCPfr4MjtorSW2H+v4JoJ8k/u13nW8wmWOs6mPgl/YXd\n/LI9PEuhJ+a5jJ3qFCx/1P7WZ57lKWzaL4vuL7ZEbYuwI8R9FVJ1Q/dbn9pmTU66agnlNsg1\nAkQFBLv41fVaG8Yo6cLoT7ONCazi5t9V+d5pz392hPtH6YSBNvAGJ7FZlJ4OhPbKchFDP5Kc\ndJ7F0DPkwXE2NkrL9vD7OxVe1u+ear98uMVh9L/915v//aVv3SWZ1yxKW9of55eq6tv/9DSd\n7HIsOivpmgthXh04BgS7OIVV3PrHmqQfpTOZCX9rG9kVqvvxfj2saX4l78lhyVcbf2M0gBCS\nMd4sSnd3dY9h2edT3bM5WOs6uHxeJz6xI1TlU8/KM/1+hmNKJpvrMPhEyi7Zu9r70Zbu9Rdn\nXtVPqU71dHkefYHNz8p85DcQ6UCvINjFgKqq1PftdynXC3pEM0D5Oi2sNd55CGk483eF9tlJ\npiEwrWpQOKQov+zsblDV+Rbzw24XBwOvg4Zf0hsC2r++Dq9rEGfnmv56pnP84JhxsTOwdVnj\nkxbKenHGVfNTz4/6+TVfIPDRGn7bboIk0n93K6Q6cCIQ7GJAURSn83umRIQ2dhM0weaf6u4U\n8UnntZoLdwn7w0M/GW+bYcyKLeAYawTxtVB4pyRn09RnmWl5NHzIDAphGX9QEXl1f6QlpCk6\nznVQzyxMmlfAGX0rRIQQahLqm8X6ZU1PllpH3Vn0e4aIfpAVvjnQ+czrWFHtC2fb558Bk+rA\nScBnbgxomsadfFhKxy33V7uvyiQTeT6ScCBccfZOXdBLVkGqGxTqVfUfgdDnEWGCiX0yxT3N\nxNpPrQo3SGh1fvWRstC6elHH6PIRltm5pvHprJsjaaO/+JIuHgjt3tq9YVdgu4nkSqwj7ijs\nh1Sn64EV/w18uIYtzE296yeU0x7l8wPDgWAXA5qmnbyOnVgR0QJq+v8l8DisVCtUzt1JMMSI\nzVO5Eig+bHA9i143ilIqST6X4j4Tto4YHLpF/e/bQ+8fimRYqXtnOOYXcNl2g8+iOyKo+v+f\nvbuOj+Ja+wB+1l2zG1cCwd3dpXhxK1Kgxd1Li5ZetLgVimtxKFLc3SEQQoj7uo+/f3Bv721f\nSpDszs7O+f7XZsM8n2wy89sjz5ny4huURCPE0YOjx9ZRN+Jyij/JehJfFy7ZRNgcyvbNNL3b\nc0SsmNSGPhMMdjTAcfz9I3amA/l8vVCUwODlaIXrMnlaQdk7dXhyttzoWeug0zXHbK0oFIxT\nKQYq4PvNFhhJtd1fiFNgRDX5qGoK9qz4chKOc4UnThceEXOlsxOWh4rCvXQhz9OkvDmrBKH6\nkNljhNHeugoUeGCw8zWKogAAAsH7jtAxbssJ+iqMw9jFKWia27A9J3h4FEx1Ae+Uyz3XbO0i\nk8zSqJn6+wp9vFvZ6PjzZgdG/dFTH8aaP3MrZl6XvjjZ+QIA0CSodafQ3kq+V9a6kU4XkpRa\nsHSzqGRM6LzxHHjUHvQx4K+Lr+E4TlGUVPqPo3HWM0YsH9H2YOoxYmi6J2NcEk/FD50cS3ct\nkHf1yC98imJtpZLJahVMdSyRbsU3PXbuTnTVChPObahiT6p7Zn+4LWstQRGjYqeVkVcs9iNf\n/+S+/6xgyWYKw7hyafD0YTDVQR8L/sb4Go7jAID3rLFDM93iUjJJBbkPiyo2SKr7VYt7XCkv\n8qdSXBlb7vhsQwGwzGp7jmJPUWyWRtVTLoOpjg0sHnLFPcf2Z06NmDunoapfeQavFfkoRrTw\nnOHEmcKjsdKSw2ImBQu99ambwjDL/lO2k5fE5UvqRn3FUyu9dCEosMFgR4/39LHD89HiPifa\nR0g3mdLlEVfKK3WqmjASLp8PTAUEMclovo+gHWXSORp1d7mUmb+t0MexIOTgk6ZXJnxqHUWf\ncjK5kC1v++mCw0fz93EAx3snSbxFEWTBvza6n7xUtm+q6QX3SUCfDgY7v2O/apHVYt4HNawA\nNWzKRtLcZW/Whqku8OAUdcjpfo6hL1E8h8D3hOgqCeGDJ/DZEPJBPnY5AzmT6nHj1Ka22trh\nbHnfnYRje9a6u5brDbUt+kQMEXG9dVsj3R7r4bP2M1cpBAmZMVxStZyXLgSxBAx2fofyEIzr\nD0I4iDe9n7ge2RUNNeIyDCseKtJBp+tXu+MNhtcRi6L4vK8VMpjq2OBOLjr8tNmCkFVDBF0S\nJD3LSaNY080EAHDNdP6F/cnwmMk11fW9dxXT1oO2ExcBAIrm9VRdW/ODg7x3LYglYLDzNYIg\nuFwuJ7BOWEob/MyT6Cx1rKq8PmxEHGi2253/sljbSSVLtJqywvft5oYCA0ZSVzKR82nI4Vfu\naqGCZc3UISxbL2vDLVsz1zyzPyqvqOzVVOe4fMd+5qrqy1bypnUE4cHeuxDEKjDY+RqKosL3\njnZQBOWzYoqFcVeu9aQhZnVZmOoCDEJR443mi27PEKV8vErJmj5lrPbdFeveRBcAoHa4cHR1\n+bdV5CxpUEdQxEvH0yTncytmvmO5JuKKv44aVUZe0UuXwwuMxk373Q+eS6pXUPdqDw9+hYoR\nDHY04P7zOUsUTnmSXAJGnZlt2punaqsLGgD7ZwaaQ07XJbdnSZCmnZTZZxZDH4KgwE83bYeT\n3L3KScfWUARLWRQ1Xjtfrkid7yZdOmFIlDi2bXCXpkFt5HxvrXW2HTtv2n6YH6oLnTtOXK6k\nl64CsRYMdv4lY+xL0kVIKjPmNEAsF3E/sodMiqW7EKiYpWD4Gqu9u1wKUx0bvDbjC27abmaj\nE2spvqogFTG2O/onsOHWhSnfaQS6HxKW6oUhXr0WkpxmO3HRdeuRonk97ZAesEcd5A0M/60i\nHLmvk9Kt4qhyZSPkgfD50nHVHDYtTlKeGU3sSCeR/f1rCqd0X8PhuoByxOmaY7YG83iDFMz4\nVYQ+2Qsj9ttL97anznA5b31rTeNoEd0V+Y6HdB/I3X7bfFXEFc8stchLx0i8RVjtxnW7Xfee\nCqPDdaP6SetW4/DZtXIR8hmmBDss68KGxRtPPM7n6ErV6T56bM+K6rzzcwcNXnA6HQEAAFFU\n87Erf53fOZrJa7vdTx3IG7eyjY7uQj6U7bzJtDcvZn05noIpv0jQ+xAA3EOQrXbnJbenk0w6\nTa1U//OyAYjprmUhB166T6a41WLulNqKQZVkQnYM1GV7Ms4UHrVi5nT3GxfhaBfcrYW+vYzn\nxc8whMVWsOgXvNAUPHmItFZlEFib5yB/w4jnMfZ8dbvGY84a324quHT64PbfHv466PbQWZc8\nmtINW1bUeZJvXT2/qEtj44mHm9oydwG/+WC+IFgoZcg8LOkkMse/lNdTB/ULo7sWqBi8xvDF\nFusVDxLG463VaZtKYDPCgJVtJ8acNT8uwOpECGfUU/YsK5XwAz9qkBRx33rruvlCsvOFXhgS\nJy1VQVG1hCwhXlraexelCKJgwTpP4muuQq4b2U9Spaz3rgVBbzEh2GVtHDbhrFFde8KKJUPr\nBhnv7pg+9qeFfScBbpmRpy+tbBnCBQDYHvzQqt68X6eumdT2uzJ0F/yp7JdN6s7BHAEz7rAF\n6zNxA1b6Unm6C4GKAUJRgwoNai4XRrqAl27Fvzph4gCwu1NQrTAm7dP6HDiF//R6eqoruZKy\nRnNdu2ZBX6gFWm9flMIww9rd7qevggZ3lzWqyYV/WZBPMCDYmU4du44JWi86tvSrYAAAKLng\nuDA1ttteV/sZC9+mOgCAstrMGT2Wddpx8ZLhuzKMmcr8GwqjRHHMWKhOuknL0UJN1xBhFLxV\nMZuJJH+22B6hqJEg9wTrI+G6n4CWZMK7HjIohJzdHYPi1Ay4/xeLAiT359R5hWjetJI/Jsh8\n9FmUwomChRs9L1LUPdoqWjf0zUUhCDAi2BUWFFAgpmbN/zZvVNWpUwbsLSjzlyMOhLGx4QAY\njUYAGBvsUMZ0sHNcM7se2aOWenEKA/KBlVb7ZrtDz+M2l4h/1KphqgtgKEHNv2E78doj4nMu\n9w1myXI6AECmO21l2o8CjmBWwrIocaxvLuq8+dB68Ayanh0yc4SkMpx+hXyKAcFOp9cDkJyW\nhoDK/96uhSQmpgDgSE9HQc0/JxKwN2+yAKivY2qqy1+R4U50iMsy4zwu5x2ruKRUVpN5Z9pC\nbxkJ8neXe6PNPkyp6KeQwU0Sge1mNjrpgsXsIUdWk3coJWFPqntsu7chfalOGDw6boa3W5m8\nRRGkZc8x65FzooS4sB8niBLifHBRCPpfDAh2Qa3a1eGf3TOxfwPd4r41dY6nB6aM3lIIADj0\n09y7rea/zRb2+3N+/M0NKjRpzNSD9kz78kLGRCtbMKB+3ICa9uXJanqxNQDkPThF7Xe6llls\nGAD9FfJRKmZs1oE+2Qsj1v+EsbxOsLdTUJSSFYOyKImkuJLeuF5dNv4RJo6cGj9fyPVJGxeK\nMu86ajtxUdOng6pLa19cEYL+HwYEOxA7bO38A02n7R/WYP+wt/+HEz5o/Zi08dN+bFDuXNvm\nFdX2x2d/v5uNBnWZ8S0zd05QCImkuMTDo+gu5ANQIKX7YywfDZkYQ3cp0EdLwrBpRksajjeR\niKeqlaE8VjzmWYggwd1cNMuO38pBz6cjMUr+vs5BLGk7fMdybWfWBgdh1wp0CfJyzYLa+izV\n5c1djSS+DhrcHS6qg2jEhGAHRFWnnntYedXCtUduptilUVU7jpszsU20ISKvY/+Vt49svw0A\nAMLoNgv2benN0IlY0k2STkJa2e+bwVIgbehz10N7iV2VJOX8vlror9ba7Kus9tICwXq9traI\nRX1oWeVkiudKJnIrG8m0EyIep36kcEAF6dAqcjakOgpQZwqPHs/fX1pWoXfEYN/Mvf7J/eiF\n59mr0DljxOVK+fK6EPQ3jAh2AABRXJtJ69tM+t//Fd7+57sZ4+7eeJhu44eUq1O3nI65zYkJ\nBw4AAFx/v/Oi2R7T3rzIxQmqdgyN0GzkoqgtdsctD/IMxbrLpNM1KgnsjxqIbAj56xPnqvuO\nSsGCjqUkTWNEVRl16vRnSna+WJe+2IKZaqkbDIwaKeb6tMMAkpxm3nFEGBsBUx1EO6YEu3fj\nyGNqtYqpRXcZnw8vQAEAwkh/bx2SuyCVrxPq+sMDxBjDRJJd8woLCeILqaSzRtpRKhHAVBdw\nXDh14rV77X2HBSHH1lCMqi73+w+Jxey66cK+3K1agW5K/LxQUYRPr01Rln0nrcfPC2PCNX07\n+fTSEPQuzA52AcP93MmT87gKv17wRBGU9URh6NQ4rsyv64T+1zyz1U1Rp8NCYCuTgGR0k6vu\n2/e/cKME1aW0ZEItRSj7/jxTXEm/Zq6qp23aK/xrr54M9k6mbYdtv19Ud/9C1akFR8SiIVLI\nbwVOsLswq8ncyyBu4JYtAz9ie7nZbJ45cyaO4+95zYsXLz67uiJYTxaKSss4/r0IxnnXipsw\neQPmntnGOq8w7JzbM02thKkuIKVa8HHnLTkOYkodRceSEq2EjT1rENKzIX1ZhDjm66jRHODT\nW6jj/E3TtkOkB9H07qDq0sqXl4ag9wicYFfw/PLly8DQxEl3IUUgCILzt7kwCjiuWcJ+KEFT\nRR+GAgUrM3lqPlOOsmUzhKL+cHseIOh1j6eSUNBZJqW7Iqj4Xc1EBp80RSn5uzsEldIGzp38\no7xyPv8lY7kNs45N+M7Hqc568Ix5z3FpnSrq7l8IY3w7+QtB7xU4t4NG048fHwiUCR/Xg0Oj\n0axZs+b9r9mwYcPVq1c/o7S/IEmS99ceE64ndtyMSav6b7Nf0kmkDU20HCuIWV+O7lqg98nG\nifsIusRqs5BkbZGwolA4UaWUwUV1ASfFgg85ZWocLVrXWstn4zgdAAA8st3dnLFCLdCOTZgZ\nIY722XUJk9X18Lll/0lVx+aarzoD+PcF+ZnACXbh1dszdEk/mubmqfiyav47EmbclWs9Y4jb\nXkHTxaftA6CPcsHtGWs0cwFoKhFPgz3qAlSSCZ9zzXo3F41T8Ve11LAz1bkJ1/H8/WcKj1ZU\nVvsmeoKU56MDeyiCMK7f47h0GwAga1BD3bcjTHWQH2JasKMQU+ab1KxCmwsh+WK5JjQqLjZc\nydw+J//G4XH8ttcJYcdzF6TqBkXAVOfPbCQ5wWhuKRH/S6sWwodNwMFIKtmEr7zvuJjuKaUR\nrGihaRQlEvNZ+kavTV+U4kxqH9K9c2hvn83A4gXG/AXr8LxC7aBusnrVeGr//SgOsRxjgp3r\n1dGf/7Vq5/GrLw3oX77AkYSUb9C+19AJY7qXg39oXmDYkkN5iJDRvpvpgD7WFY9nrdUh4IB5\nMNUFHDtKnUvzLL5tz3cSoTLegsbqdvFi1ka6p/YHx/L3pTiTxsR9V0VZ0zcXpTDctGm/49Jt\nXpA6fMl0QWSob64LQZ+GGcEu//jwxj3XJ7kB4KviqtYqEaLVaJRigHmc5rysNy+end088+y2\nNa0Wnzw8rgpcJ16c0HRP4YZMZRudMMbfe+yxE0ZRvQsMz1GsnFCwRqeFy+kCCQXAnGvW3c9d\nJAXqRojWtFKzquHw/7pqOnfNdL4Qzbfhlnhp6YklZpdXVPHBdSkEdd56ZDtxAcsp0PT/Utag\nOg+erQz5PSYEO+tvI/quT5I3nr5l0Yh2NSLlf19UQrkzLv0yfdiU3ePbjqv4ZmNzmECKj+Om\nBTdgEfNL0l0I9A4eivrOZHmOYtuDddVEQrikLpAgBLXmgWPnM9fYmopBFWVyIUsjOwWoHVnr\nLxnPVFBU7RzaW8XXVFRU43J8sbSQIsj8H9d5XryWVq8QNKSHqLR/Ny6AoP9gQLBzHt911K7s\nvfX4gi7v/qjEkUQ3HbPzNJmRMH7rxuOrmndn2CGYniQXT+Wnb4TtnFFUQuL/R2Kw0C0PMtZo\ndlHU9xpVTdgWNYDkOIgdz1x7X7jcGNW9jHR0dfYeyvzEdn9r1hobbhkUNaqBtrlPG5pQlPXA\nKU9icvDkodLalX13XQj6bH6aJ/5XXnY2AeIqVXr/ADgnrnmzEuDamzdZAMT7qLJi4rxvldf3\nx66/WAFq2p8ftSSB7kKgvzvlcv9gtpQVCOZr1dF8BvwVQx9ob6Jr7UMHToKhlWU9ykp1rOw5\n/JYVM69JW1hGXqFv5DfBQt8ta6Nwwv34hePcDde9p4rm9aS1Kvns0hBULBjwSAgLD+eA83fu\nmEBJ7XteZnz0KBNwmgYz8HB6EvCD/G5jL0VQ6UOfc0WcoL5hdNcC/dcdBNlud15ye9pJJbO1\naglcVBcQUIJ6Uohteuw8l+rpUloyuoYiyr8PGPQqgiKSnM93Zq1XClTfxEzw6SlhJJn3w8/I\n6wxRXKRudH95Ix/tz4CgYsSAYCdt26uD8tjhkW0ncNZ9171q0P8vmbImHlwwdOwxt6RNj/Yq\nGkr8PFgOIi7roz5MH86T5LSdN8UfqAxPhvUfKRg+uNBUks+frFb2U8jhGxMY3ljwr383ZdoJ\npYi7rb22fiTDFpMUI4T0bMpY8dLx1EU4S0gThsVM8vHZr57nr5FXaeGLpgpLRPnyuhBUjBgQ\n7EBQr7U7r6b0XPdzn2qrR5aoUqNy6dhwnUIq4CAOm82U9fLhnYevjAgQlRiw45f+erqr/Xie\n167QqR9xvq0PkG7SuCOXrxGoWgXRXQsEAAAkAPsczh12Zwk+f2+ITgQH6gLF4VfuxbftQh44\n01NfUsOEG7J3UIDKdKeeLDj0yHanW1j/Gqp6QUIa7ub2Czf5ITphXKTvLw1BxYUR9xFORIe1\nt560X7dw2eYj1+6efXP3r1/myiLr9Bo4fuaUHuWZuhGdI/Cj5zRFUEmN77oTHWEzSvht22RW\nuY+gv7vcexzOJhLxdLUSprrAQAGw6ZFz0W1bl9LSaXUUGjFLl9ORFLEje8Nl4x8AAI0gaGDk\nyPraZrRUguUUuB88U3dtA8+TgBiNEcEOAADkJdtO/qXt5F+QwqQniRkFJrPFiXHFcm1obEL5\nsnEauCmwuFAgZ1aKJ8lZ6lQ1RUMN3dVAwESSIwwmPY87UCGfqvbfA4Whj2JDyG6HjWlW/OtK\nsml1lazNEc/sD4/k7clwp/aJGFpRUTVERNvBkJ7nyYZV2wGXK60F98BCzMaYYPcfIn3pmo1L\n011F8aEIChAU3VX8G0VQOd+/zl+ZEf59CZjq/MF1DzLRaFZwOXuCdQouS0d0Ak+SCR9+xmzx\nkEe66srp/G7jlG+4CdeJgt9OFxwpLS//bcyE6qq6dBbzJKngx7WCyNDQOWP5IQzcgQdB/4Nx\nwS7QEGaM9JCCML9YLv2m9xPrSUPE/JIh42LorgUCm+2OVVZ7BaFgWZAGprrAYPGQh1+51z50\n6CTcnR20rE11OZ7MXzKW5yKZbxvU0VuMefcx66E/hLERofPGcyWwZyfEeDDY+QWuiP7Htv2y\n2XraGLOhHOxv4g9sJLnMYhuokA9TymGqCwAUADueObc+dWXb8dZxkrkNlWq2Lqq7aDy9O/uX\nIIH+h1JLw8U0bz61HvrDeugPTb9Oqs4t6a0EgooLDHY0QzMRAACH7mBn2pOXMe6lsoVW2wue\nb00nB0k9Q9HVNvt9BJVwODDVBYYrmciu566LGZ4eZaSDK2ni1Gy88WZ7Mlam/liI5nMAp6nu\ni74RQ316ksS7UDhhO3VZ0bI+THVQIGHj/cWvIGlunpovKiGhs4ZUd9o3z7XdQyMXluLwWLuM\nm35mkhxrMN1F0Fg+f2mQpppICFMd070244tv28+leaqGCFe11LSOY+NMX7LzxeG8XSnOV8Gi\n0Oklf1IJNL48SeKfEDaHceNewmJTtm1Cdy0QVJxgsKOZaW+uMIrOez3hIDLHvRSEiKLXluWy\ndW6IdgQAa632Uy53AUEsCdK0k9IZ9KHikmTCex01Rip4W9ppG0aJ2PmZKdn5YmHKdwqeql/k\nN1WVteV8v2hKRTpcuVMXUQiqHzdQEAUXn0ABBQY7miEpbv1QOpth5i1MddyylthTCaY6uhAA\ndMsrTMKwHnJpL7msjIClC+oDBkGBvYmuu7nozWykpIa/o71WzGdnqAPZnozfcrdFimNmJ/xM\ndy1/Ydy4l7A5IlZ8z9fB7f9QoIHBzg/QF6iM23Pyl6dHryijbPa+c3gh7/FQ1Hyz9TWObw/W\n1RDBfoyB4JdHjhX3HM1jRG3jJaOqy9mZ6vKQnHXpi7Lc6WqBdnD0WLrL+S8832A/e91544Gm\nX2eY6qCABIMde1lPGjInJAX1DdN9HUF3LSxFAPBVgSEJw2dpVDDVBYbfU9yr7zuGVZWNreEX\nc460cBOulanzXYRzdNyMCooqfI6/DEITFlvujKUUQah7tlN1ornNCgR5CQx2LEXhVNb0ZEWL\noOgVZeiuhaUeoeg4g9lEklv0QdVhqgsI59I8E85b2sZLvq3i06Pr/UoBmrctc60Dt0+KnxMt\nKUF3Of9BUZ7E14XLfgVcbvjCKXCsDgpgMNjRjEJJWq5bsCYTzfTErCtLe6cVFiIBmGmynHK5\no/i8zXp9vAD+GTKeC6e+OWW6l4tVDxUubaZm5xnLGe7UvTmbkxzPpTzZkOhx/pPqKIIwrt3l\nuHxHXK5k8NRvuTK4OQkKZPCJQicKo9AsRBDi62MnCAeRtzhVNyBcXk/t40tDOTgx0Wh+jmHT\n1Mq2UokaNjRhPg9Ozblmu5WNTq+n7FhSws5UV4Dm/Zg8VcwTD4+dXFZeScbzozFL068HHZfv\nBE8eIq1dhe5aIMjrYLCjkyfZSaGkuKzMx9e1nzeSbjJ0WpyPrwsBALbYHZkEvi9YV1boLwuP\noM+RasG/PW3OdhDzGql6l5PSXQ49Ul3JK1J/pAC1uOwmIde/1hV4EpPtZ65oeneAqQ5iCRjs\n6EQ6SQCAMNK3fewoYD1pEMVIBCH+df8NeAQA2+2OXQ7nVLUSproAkGknFt60Xc5E9FLe4S66\nBC1Lb6d3LdcP5+1WC7TTSy7wt1TnfphoWLdLVDJG1bU13bVAkI+w9E7kJ7BsD1fK4wh9OnNj\n2ptn2psXuTTBlxdlOZyiVtnstzzoCwwbplQMUPjRLBX0CRCCmnnFejjJHSzjTaql6JwgUbFy\nraoVM98wXzqevz9BXq5r2FchonC6K/oL9/1n+Ys2ikpE68cPorsWCPIdGOzoRBEUT87z5Sle\nrkf2vMVpisYa/RA6uyKzioeiFltsex3OrjLpdxplJaF/DWlAH+tBHjr7mi3Nis9pqOpeRiJk\n6yl8BEXsztmUaH8cLyv9bfRECc+PpqEpDEdS0s27jgljIkLnjOXAAXKITWCwoxOahfBUPn0L\nUro+EkaJIxfC4TpfoAC4j6Cb7Y6bHmSaWvWVwteLKaFiRFLgbi56Jxfd9tQZr+bv6xxUNojV\nceFg3s67lutfR41uoPWvhnCk25M/ZxXyOl2UEKsb3hemOohtYLCjFUHx1L57C2wXTFg+Gre9\nou+3a7DQKqv9hMudgeOxfP5YlQKmOka7l4fOuGRNseBRCl6bEuIVTAnQAAAgAElEQVRJtRRq\nFh/BR1DEBcPJPwqPfhH8pb+lOte9p6bNvxEWW9j8CcJSsRwee98miLVgsKMT6SF8eTnj1hx5\nHRVsceIDj1B0rc0+SCFvL5UkCPh8Dktn6wKAE6NmXrEeS3YnaPlHu+oq6Nk+/OPA7fOSJxmx\nwgaa5t3C+tNdzl9g2fmGNTuF0eHBU78VxsIDdSCWgsGOTp4XTmGUj1plmvbmmQ/lx24qD2DG\n8CYKgNseZKLRXE0knKJW0l0O9FmcGDXijPm5AVvVUvNFvBj+6Thw24rUH92Ea07C8ghxNN3l\n/BeF4ZYDpxxnr/Pk0uBp33Ilvm01AEH+BAY7OhF2QlrZFwdKkm4y91+p6g56ba9QH1yOtSgA\nFlps2+yOskLBiiAt3eVAnyXJhA85aTJ5yM1faOtEsH3LC0oiyc4Xx/P3mzHjiNgpfpXqHJdu\n205cwHILVZ1bypvWgakOYjkY7OjkvGVRNPHFkYVpg59jWZ743yr74Fqs9Yfbc8uD7HE4hysV\no1UKOLrDaLdz0KmXLFoJ92AXXbCU1eu0KEDdNF/ambURIT0hovCh0eNLy8vTXdR/uZ8kGdft\nFsZHhS2YKIyB068QBIMdfQgHQbhIaRWvj9i5nzssxwpiN5cXl/KjfgQBxkaS4w2mGD5/gko5\nRCmHqY65PDi19oFj/UNH1RDhhFoKNqe6FGfSTculLHd6svNFA23zDiHddcIQuov6L4ogTJt+\nc167J4yPDvluBDwBFoLegsGONqQDByQliPD6rEHB2kxBqEjT1Y/uyAHGQ1FjDGYVl7s3RKeE\nZ78y2ek3nokXLDwOmFpXObgSqzcyH8zdebLgYJQkNlpSoktYvwRZObor+gssp8CwajvyJkPT\np6OyTSOOiO1z5RD0JxjsAp/1pCF4VBSHD0eRvOUhgt5GkNU6LUx1jHbitXv6ZWvlYMGqlpog\nCavfyhRX0unCw/W0TftHDhNw/C4zuR+/NKzZCSgqePJQaY2KdJcDQf4FBrsARzoJvBCVVoXb\nM72FAGCx1RbB59UXi+iuBfpEqRZ87wvX5sfOL+LFPzVWy317yp+/ee18+UvGz+HiqIGRI3kc\nHt3l/J3jwk3D2l3isvH6yUN5Sng6HwT9HQx2Ac523sjhcyQV4O3PK2wkOddsTcbw/cE6MWxW\nx0A5DuK7y9brWYhCyB1TQzGmBtv/Um6ZL2/M+DleVnp4zGQ/THW40WLaclBWv5p+/Nd01wJB\nfgoGO9pgOQgAwNsHxWJ5qChOIgj2u8mUAJCDE1NM5ucoNk6lKAuPLWKgo8nuOddsajF3YVN1\nx5ISeEgBAOCB9XYVZa3RcdM5ftnx0nH+BofP1w7qTnchEOS/YLCjDZLi5gcJRHHe3MlFAcuR\nAr4eprrit9fhXGKxqXncFTptIzgJyzQkBVbfd6y6b+9YSjKvoUoq8McQ42MGNP94/m/3rTe7\nhn3ln6kOAIDnG4UJsTy1L9p/QhBDwWBHJ46A69X7J+km7FfMcdsrePEarLTIYttid3SUSSao\nlCE8v5uugt4DJSgHSk25ZLmSiYyvqRhRje1zr2+RFLkufYkFM7UN7tpK34Huct4Nzchx3nqo\n/aoz3YVAkF+DwS6QkQgJABBGw/ZOxSkZw7faHZPVyoEKOZy7Y5BMG3Eixb3lidPoJqUCzvZ2\nQfA8ibdQEjmYtzPTnTo74edwcRTd5byb9dh527FzgrBgWf3qdNcCQX4NBrtA5rxj4wg4olh4\nwE6x2W53LrJYo/j8/nIZTHUM8saC9ztuEnJBsxhx73LSUBk3RAaHWgEAwIqZp70cjpCezqG9\n/TDVUTiBvHjtvP7Afu66vFFNdZ+OXAWr+wtCUJFgsKMNYce9vY6lYHWGIFzE18FhieKRguEr\nrLaectl4lZIP98Ayhwunxpy1YCR1uodeKYKB/C8umc6QFDmv9Eq/Ov71LQrDDWt3Oa/eFcZG\nBg3vo2hej+6KIIgBYLCjDW7EhFFeHEszH8p3XDGX2FvJe5dglaseZLTBFMnnjVMp5FyY6hjj\npRFbec+RZMK2tw+Cqe5/2XDLH4XHzhlOVFfX8ctUh5m3H3HdeKAfN1DWoAbd5UAQY8BgRxss\nH+V6bTIIy0HSv0lUddCr2ui8dAlWOeZ0/2ix1haJVug0sF8dg9zOQYefMavF3F++0NaFK+r+\nw024juXvu2I6K+KKv9B3aR/if91DSNKweqfz5kPd8D4w1UHQR4HBjjYUQgq81ojEeddKkSB2\nQzl/7VrAJDsdzh/N1uYS8aIgmOqY5GE+NuCEqVooPCLsLwqQ3J9SZthxW6eQnq31nYVcf8y7\nztuPnTceqHu2lTetQ3ctEMQwMNjRBnnjEpfy1ipg532bpLzMeyOC7HHM5V5ssXWQShYFaeiu\nBfogFoR8UoAdS3bfyEbj1Lwd7YNg5+G3CIp45Xy+Ou1fKr56ZplFQUI93RW9G5qWZVy7Sxgd\nru72Bd21QBDzwGBHGzQbUXfw1o0Vee2WlIcNuj6XgSCXWGxtpOIFWpjqmOFxAdb3mNGNU6W0\n/H7lpa1LiGGqe2tfzpY/Co9RgIqVxI8r8b2Sr6a7on9k+/0SX68NnT2G7kIgiJFgsKMTR+it\nZw7y2qVopvXSP84SmTgx3WQ2EsQUlQqOfDKCC6NW3rMHSbhHu+rUYhjo/s2A5m/PWv/M/rBH\n2ICKyup+uE/if7kfv3TdeqTs0Ay2NYGgTwODHW0ojPTSv5y3NM2d6IhaUdpL/37AIwA44XSt\ntNklHM5KnRbO5DHFjmfO61nomBpymOr+dNtydXvWOgVfNSR6XD1NE7rLKYLr9uPC5VukNSqq\nOrWguxYIYioY7GiD5SCC0OI/Y5QiKOP2XE23EHld/51q8WcYRXXKK8zA8XZSySS1Ug9PDGOO\nFAveNl4MTwn705nCowdyt1dS1vg2eoKQ6+8nGrsfJhYs3SytWUk3ZgBHAJ9NEPSJ4B8PPbB8\nlMIofnDx70eznTMhqe4SuysW+7/MEvudrlyC2BmiqyL0x92C0D85m+o58sr9bVWY6gAAoADN\nO5l/8IrpbIeQHp1CenE5/j6EaTlwyrLvpLR25eAJXwOuv1cLQf4MBjuaEBQAgK8p5p8/hVO5\n81MU9dVw58SnycGJdTZ7fbEIpjpmybYTUy5Z25WUjKupoLsW+lGA2pC+1IqZB0WNaqhlwJym\n69Yjy97flV801vTvDFMdBH0mGOzoQSJeWWDnvGt1PbSXuws7P30KAoBxRpMAcL7XqOiuBfpQ\nOAmmXLRczEBEPDC/kYrH+j6DhWj+jqz1me7UaSUXlJAm0F3OB7GduCitVUk72P/6JEMQA8HP\nRvTA8hEAQLGvsXPetAoiROKycDfZpzjidCVj+BqdNgSuq2OIVyZ83Dnz0WT3VxWkf/TUywRs\nj3VWzLwidX4ekjMpfg4zUh1FWQ6c9rxMkTeuRXcpEBQg4IgdnYq93YlpX56qFTxD7BNdcXsq\nCgXlhAK6C4GKRlBg2iXL4SS3Tsr9qYmqRxkp3RXR74H19pbMVTwOf0r8vHBxFN3lFA3LLTT9\n+pv70Qtl2ybSWpXpLgeCAgQMdoGDsODuREfkYiZ8TPc/RoK84kGmqJV0FwIVzewhZ1+znXnj\nmVFP2amUBB4XBgC4ab60I2tDeUWVgVEjZTwmLLGlKNPWg1h2ftDg7oo2jeiuBoICBwx2gQPN\ncAMKCMP9vamBH0rB8C75hVwAGovFdNcCFSHHQXx72pxuxZc2V7eLh+8XAAA8sd3bn7uttLz8\nkOixIi4zfiaGNTvd95+FzBguqVae7logKKDAYBc4CjdmieIkohISugthEhKAnXbneps9ks/b\nG6xTwB15/s2GkDMuW20IefBLXSktvH0BAIABzd+Y8XOsJH5Q1CgGpDqKwo0W++nLjku3Nf2/\nhKkOgoodvDMGDjTDo+4UDLhsXz/+Ua64PT9ZrF8pZGNVShkH/uj8GkGBjgcMWXbily+0MNW9\nZcMty1PnK/iqQVGj/fn417eQ5DTjut1oRg7gcYO+7a1oWZ/uiiAoAMGbIz0IKwE4ABRjkCAp\n11OHsmVQ8f2LrLDT4awpEs5Qw/4mfs2JUSvv2Xc/d2Ek2Ns5qEYo7DII0twph3N3vXa9FHJE\n00v9FCTU013R+1AYZt51zPb7JVHpuNC544QlorhiuGgEgrwCBjt6EBZMECri8Ist2WH5KF6I\nKhpriusfDHgUABON5useZGEQ/KH5NQ9OjfzD/LgA61dB1qe8NEoBm9GARPvj5anzIsQx3cMG\nVFJW1wr8ei88haCFy351P0nSDvhS2a4pgEPjEORNMNjRp1hvbq6HdsAB/BD4IfhDrbfZT7nc\n87XqDlK4KtF/HX7l/tdNmwujljVXt4zz+wVk3kcB6lTB4TOFR0rJyk0sMYvL8feYiyS9KVy1\nnbQ5dSP6yhrWoLscCAp8MNjRAy9EuaLiXKefMzdF1VYnCIFTVB+EAuCw09VVJu0qg/3P/FSW\nnbiWhfx8x149VDivkQr2NAEAmDHj5syVifbHTYJadwvr7+epjrQ7s8fOI2wOcYUE3Q+j+cFw\noQgE+QIMdvQgnUQxHjthOVrgfgY72H2EX+2OLJxYqIWpzk8dfuWef8MGKBCl5C1qqpYL4eQd\nyPKkL3z9nYQnGxI9rp6mCd3lFIWiTFsPAh4v5IfR4rLxHAF81kCQj8A/NsYjXUT2zNeKplpF\nA7hW7INk4sRyq32YUlFVBAc4/dHMK9Y9ia628eKFTdXS4luHyminC4/sz9kaK4mfFD9XyvP3\nMwMpnMifs9LzIkU/dqCkUmm6y4EgdoHBjvGQVDeS6o4/ULl4F+0FsGMul4rDGaFkQnd+9tnw\n0LEn0TWjnnJgBRkPzr4CAAC4ajp3JG9PS32HTiG9GJDqELRw1XbkdUbI96MklcvQXQ4EsQ4M\ndoznfuLgqfjiUnBW8YM4SOqAw9VCKubDrXn+549Uz6Lb9gk1FYMr+Xt88Rkn4TiSt6eSonrX\n0H5Crl/vjiI9iO3IWcflO5QH1Y3pD1MdBNECBjvGowiKp+bDvsQf6JDTlUcQ/eVwuM7vPCnA\nFty0NYkWjawO3x0AAHDg9if2+0fy9nhId6fQXn6e6tA3mcZN+7HMXHmzOopWDQURIXRXBEEs\nBYMd4xk2ZfFk8H38IOfdnuVWW0eZJA4u5fYz59M9I89YYlS87+op6a7FLzy3P9qfuzXXk11Z\nWaNzaO8IcTTdFb0XRRlW76BwPOT7kaKEOLqrgSBWg483hiMpd6IzejWc8igaTlFzzNaqIuH3\najUc3vQrc67Zdjxz1o4Qbv5CK2b3bgmSIg/l7XzheJrqSk6QlZuVsNTfIx0AFIabdx5BM3PD\n5o2HqQ6CaAeDHbMVbMgiXYQ4AS5IKtpjFCskiA06rRxOW/sND07te+Ha/9I1sJJsYi0Fy1Pd\nc/ujvTm/5iHZzXRtu4b2K6uoxPH/LVEUlfvdMjQ1Uzuwq6hMCbqrgSAIBjuGM2zKVnfQS6so\n6C7E3x1wulZYbWWFgtJCAd21QP+187lr8W1b6zjxxFoKCetT3c+p8+KlCbMSlkWKY+gu58NQ\nlGHVdjQ1M2T6MEm18nRXA0EQADDYMZrtrNHzyhm5CPYlLsIrDFtqsVUXCWeoVbCBhv94Woit\nuGfvU042qwHb19U9sN7amPFzGXmFiSVmM2CUDgDSg6BvMi17f/ckJuuG94WpDoL8Bwx2DIZm\neYQRYkUT2Je4CIstNh2PO1uj1sHGaP7kt5euMBlvXE1W74H1kO6rxnN7cjZXVtYYGTuVEakO\nAFDw03rP82RhXGTID6NhC2II8isw2DEYlo3wg4UcHjOeBHTJwolkDO8pl8JU5z8OJrl3PHM+\nLcR+qK9UFeuhyQyS7cm4Z7nxe8FBnMLqaZoOjBrJ5zDghoxl5Rk37PG8SNFPHCyrW5XuciAI\n+jsG3EcCEuEkPv+TOZLuFsVKiqOcgGUgyNlmC0pRbaXwB+Uvfk9xT7loaR4j3tJO0SjKr3uz\neQkFqG2Za6+bL6gF2nbBXVvo28t4DBi2pFDMtOWg6/5TrkQcPGmItHZluiuCIOgdYLCjB2HC\nBBGf/UgjAU8F38F/RAAw32J9jeGLgzQxfPiD8gvjz1uOJbtrhgk3fsHeJQRnCo5cMZ3tGT6o\ntb4T3bV8BMPaXe57T5Udm8sa1hSE6ekuB4Kgd4NPO9rAKVRvW2yxXXR7lgZp6ovZOCzkh27n\noL+nuKfXVQ6uzNIGPSRFHs3fe7LgYCNtS2alOseVu85r94InDZHWqUJ3LRAEvQ8MdoxFASTF\nJaujprsOP+WmqAMOZ0+5tIVETHctEAAAODHq+yvW2mGirypI2fmZpgDJXZu+ONOd2i6kG7NS\nHel0m7cdkjeuBadfIcj/wWDHVPbLJuc9m354FN2F+KlNNoeLovrJWToy5G9SLHj/4yYHRm78\nQiNi5Vg1SiIrUn+kADkrYWm0hGGNfE2b91MopunbEXDY+N5BELPAYMdUBeuzxKVl2p6hdBfi\nj654kI12xzClIhourfMD2XZi+iUrBcCxrroYtq4KPW84mYtkLSizJlQUQXctH8dx4abr3jN1\nj7Y8LZwfgCAGYOlNNgC47tnCvoPHMr5DBo6PM5gaiUUjVfBADvrdzUXHnrN4cGptKw07Ux1J\nEZsyV942X2mha8e8VHf5jmHtLln9avJmdemuBYKgD8LG+2wAoDAKN6CCELgn4O8oAEYbzJF8\n3pIgDY/uYqBMO7Hktl0v5S5rro5Xs/Fug1PYrFfjC5H8cSW+r6ioRnc5Hwd9k2FYvUNSvYJ+\n3CA4CQtBTMHGW60/wE0YT/npP3zPSyeFU8IYuC3gL95g+FqbPQXDdoboJPA5RLfXZrzzQYNS\nxF3UVMXOVGfFzUfz9uV6ssbEfce4VOd5mVK48BdRfLR+PEx1EMQkbLzb+gPCTojLfnpLUjTd\nzRVzJeUZ0NTUZ3IJonN+oZ7H/UGjriIU0l0Oe6EEdSkDuZmNnkvzaCXcc730Qlbuljict/tM\n4REJV/ZlaJ9KTEt1gKJsxy/ww/Qh34/kwm5BEMQoMNgxkue1SxAG77b/RQCwwGxVcjlHQvQK\nLkuPqPIHmXbiq+PGPAeZoOV/mSDpU17KzlSHU/ipgkNNglp3DOkp5yvpLufjkC63edcx1+3H\nutFfcWG3IAhiGhjs6EGYMc5nLAHDjZgoXlp85TDeUafrnNuzQa+FqY5GKEHtfObMtBEX+wRH\nK1m9xNGEGXAKb6BtwbxU53TnzVqO5xt1o76SN65NdzkQBH00GOzo4XnpDJkQ8+nfnuTksXLR\n0j856XLXF4saieHoAm0upiMbHzmeFmJ9y0tZnuruWW/szNqgEQRFiKPpruWjGdbuIkzW0Lnj\nhHGRdNcCQdCngOGAHhRG8bWCT/5e+wVT1LLSxVsSc93yINc9yEqdlu5CWOqlEdv53LU30VUp\nWLDpC22dCFYvcCQpcmP6ssrKmv0jh/M+Z1ieDmhatvv+06BvesFUB0HMBYMd8+AmjPSQkoqw\nSRsAAGTjxPdmSwOxqDlcDORz2Xbip5u2U288PA6Y31jVqyzblwcUovmLU34gKKJH+EAF0yZh\nrUfPOc5d54fq5U3r0F0LBEGf7sODHenIe/Mm02Dnh1evGsZFBXDfIV2QVBcAQBABN08AlKK+\nNRgxCszXquHaOl96mI/ey8NW3rUL+Zzv6yt7lJVK+WzcJPG/LhnPHMvfp+Srh5ZcoBeG0F3O\nR8DzDOZ9vzuv3VO0qK/q1AI2N4EgRvuQYOd8vG365B+3X0i2EgCAyvOSH9VYEDPGOmHLL5Pr\nw9kv37OdNooTZALdJ87kBpIsnEjB8F/1QSE8hs15MdejAmz8OXOGjQiR8VrEif/VRMXOs1//\nxoZbtmetq6mu3z9yuIzHmD5EWE6B58Vr89ZDFE7oxw+S1WNaWxYIgv6fIoMd8Wxxq/pTbjgl\nUbU7dFAn7zsDAAAhJSMKZ05p+iL//L0lDdk+++JzyBu3tLoCcNn+NLWR5ESjOYzHqyKCo8c+\nUugi+x83lgkSLG2mrhQs5MNh0v/Yn7ONAzjdwwYwKNU5r94z/rIPUJSkRkXd8D4cIfysCEGB\noKgbc8GWcTNvgFpTL6el3Tq2Y1Ttt0/QqjNuPVjVUvJi2aQN6d6vMfAQFEVQn3zyBIV/+vcG\nktMuz2sc/zU4CB4y4TM3sxGSAlvba6uFwlT3b/lIzs7sDbcsV/pFfqsTBtNdzgehMMx5/X7h\n6u3iiglRmxboxw6AqQ6CAkYR92briUMX0Ihvfl7QKPivr+THjZgzJIK6c/a8zYvVBSoKAAB4\nmk+6k1LAcdMijGD7RgEnRS232uqKhLF8mHF9gQJg3nXbTzdtcWo+XE73J4T07Mze+Nh2r1vY\nV02D2tBdzoeyHbtQuHKbrF41/fivOXDAG4ICSxEPxYL8fApEx8a+I/9xSpSIAyA/Px8Ahm3+\nYjTHDQteiCpbBtFdCM3uI6iZJL/XqOkuhBUcKLX+oWPrU+fo6vL2JSV0l+MvbpgvHs3ba8QK\nv42eWFNdn+5yPpTtxEXrkbOyetX1YwfQXQsEQcWviGAXFh3NBxdu3LCN6fb39EYlJ6cATkWd\nzxIGanrzPFdUoXzE24Eud9qVQ4cvPE4zoZKQ0nXadm1fNZgNQzf2y2ZxWZmkImPW8XiDh6Jm\nmyzVRcIoPtwz4QvrHjo2PXZMraP4pgqrf/H+9NB6+4Lx1AvHk3LyyuPivg8TM6PrG55nsB4/\nbz9zVdmuiaZvJ7rLgSDIK4rIQvK2vTuojuwb3btO9LYxtXR//n/CcGPW5F9yRY1+aOuLfbGe\nl/umDp+07lJWo3WF54bpAPpyY882o46kY3++YubEhO6L920ZWUXmg3I+F0VQAAB+0KdMxWL5\niKgE24dMZpktuQSxSc/2YUufSTRgzWLEMNUBAFAS/b3gwPH8/fGy0iNiplZR1uRymLHY0P34\nhWH5No6Qr+7WRt2rPd3lQBDkLUUNcml6rFh/6E7ffePrlPi5Ws0QAwLsB8e0P/Xyys1Uu7zh\nklWDI7xfo/PsqOa9NudI41sM7l5DBgBxb07XEUfS+VGNhw3/qll5PVGQeGnn2q2/jWrmkj47\nMSjc+xV9LgoAALiyTxltclwxqzroi7keRllptf/udM/XqksI2DBES79CF3knF/2hPlxxAQAA\ny1PnJjtftNJ37BX+Nd21fATnjQeGFdtE5UoGTxnKha28ISigFf1ojOq1+25I9UmTl+y/fyED\nAAAenfodiKMaj1q9emH/Cj7YSeU5uWlnDrf8hDM3lzZQAACIP9auTSTCe/52d++X/24C2rHX\nkCHtBtbouG3Wz7cHLQ7cc6txI+ZJcUc20NBdCD1cFPWLzbHBZh+kkHeVwTY73oUQ1MZHzvNp\nnlQrHiThNoqCDbHBytQfXzqejYidUkNVj+5aPgKFYuZth6T1qunH9IfNhyEo4H3ImAc3rOnk\nXfcmbsh6/iQ5146L1BGlK5UNlfjq/pCVkoKAsr2GNvj3EVo5z59bgLrrwC//0tpd12F498ht\nS27dyga1fTCKSA/PCwcgKWlNNo6dJKLYCIPJQBAjVYphSnicmnc9zMeW3bHfzUXblxQPqChr\nGiNSi5gx4eglJEWcN5x8ZLs7IHIEs1Id6fZkj51PWu2avh1hqoMgNigi2OEOo8HJ14SoRIAr\nj6xYL7Lif79GukwFNp46VOXlcX2lUgmAFUH+898KpRIAifT/Ddjw+XwAkP++LgChmQhPyed/\nWp8UhjvgdHEAOBseEgYPmfCyvS9cc6/ZKugFm9tq6kfCgTpgxcx7c369Y7nWUNuicVArusv5\nCGhGjmnLAcrlDl86na9j6Ug/BLFNEZ/CXy5pHBYz8uw7v2bZ2S0srOMvuV6o6i+C69aLB683\nztqShgMAAFC3bFdfkHvit+vu/32V+9beo2lAU6VKtLfroZH1tEFSgY0L2A85XXsdzkEKOUx1\nXmVByAnnLd9dtraNF+/ooIWpDqewg7k7J74Y8sqZOCJ2yqCoUXRX9MEoynnzYe70JYTBrBsz\nQBAZSndBEAT5yLtH7Ex39uy+YwQA5N4xAeLV76tXp/39JZTryc67AFRAUS9XCEDViUu+2tp1\nx+DqtS5Omjy0W+vaI9YuOtx0Ure20qXz+jdM0BP5z85unjVz5QthtfnjWgTygnoSIaXV2DgP\nu8vh7CKT9lcwYc8zk824ZL2Ti65ooYbN6gAAuUjWtsy1Ge7UNvpObfSd5XzG/OlhmbnGX/Z5\nEl9LKpUOnjYMnioBQazy7hiUc/LH0XOe/+e/ctePvvvu7xZX69w6yit1/YWm85abB3R9R67Z\nMaPPjhmArwiJ0HIFeZcW9W246M8XScsM3HV4ejlWLwQKTAQADpIqBffAepPZQ44/b7mehWxs\no20aw/aBOgCAh3T/mrnKhBrGxH1XRl6B7nI+Am605ExZJAjTh3w3QlK1HN3lQBDka+9+WEZ1\n+deOkhYAQNah6dNPRE/8dXiVv7+Ew5cFl63buHKoT5IUL+rLZVfaTbp5YO/xS9du3HmWmm8S\niPkYIZAqgyJLVazZtONX3wxoERvwowwkRXcFvkYB8IPJkkcQ5YXw4CNvsSDkhoeOB3no2lYa\nmOreemp78Mb5amTsVAalOk9isv3MNTyvEJBk6LzxXFnA3xAhCHqHdwc7VaX2/SoBAMAbz6kj\nxlJf9uvnD8flCMPr9plQt88Euuugj+eFU1ZTRXcVPmUiyENO12yNqgY80dI79iS6frxhc+PU\n9LrKlnGwwxkAAOzL2XLddKGysmY1VR26a/kgFE7Yjp2zHDwjjA4XV0xQ92oPUx0EsVYR01sl\nhuy6NeSfvvhodZ85xoE7ZrVi43J+WuAGTFKWXevM1tjsHAAaimHg8AoHSs2/YetQUjK6ujxC\nATemAABAiivpTOHR1vpO7YK70l3LB6Ao26kr5l1HAUkq29aPCiEAACAASURBVDZR92rPgYsW\nIIjdPuAWgOdc273nXJLBQ/xlHpByPz2w/6S2cj4Mdh+LIiiuhMvhflJPKTZ1orrhQfY6nD9o\nVOHwTFgvKHSRHQ4UogQ1sZZCL4WrUwFO4a8cz7dmrY2Xlu4e1p/L8e/fOpJ03nxkOXAKy85X\ndWimbNeUp2XXcD4EQe9UZLAr2Nu7au8DBe/8GlfbaEz7uGKv6dPs7cbpfRCUn/X02eyPWBOT\nmppau3ZtHMff85q3vfEoqvjWt1GAHyQEH5nQCDtO2HGeyr8fNsXnuMu9wWavKBT2krNrkNI3\nHhVgUy9auBzO7931MNUBAGy4ZUnKrCxPerys9LDoSf6c6nCD2bzzqOfxS8LhlNWrph8/SBjN\ngJMUIQjyjaKCXdKmBQcK9C1m/zK7leDM9B4/Okb9vrqT1PzqwrrZC5M6HzwxtjyzHwkxMTH7\n9+9/f7A7ceLEihUrOHQPlbke2QEAPC1bOhesstoi+Pypasb0mGAQCoDRf5hD5bxZDeQJWjhz\nB1ASnfNqIkoiM0r+q6SsDN3lFKFwySbC4VR1bSWtVZkfHER3ORAE+Zci7um269eegpIzl8zq\nVBmA8v3qzBvxxlalbhtx3Uat60jrVRw6p8+LJTX947nQbae9/VbAE37cEaJcLrdJkybvf01K\nSsqnl1V8XPds4lJScWlWDF/dQZBsnJiiVpURsCXI+gxCUNMvWfOdxNb22ni1f/z10oSkyDOF\nR9PcrzPdqXbc9lOZtUFCPd1F/SOKIJDEFPv5G8jr9OCp30prViz6eyAIYp8ixtsKCgoAiI2N\nBQAAoI6NVWFPnya9/cbSQ4c2Tvl14/n3jXX5El8sl8vlEiGzRxDfA81GhLESDo8Va+y22J3V\nRcLGYth6o/gtvW0/m+ZZ1FTN8lRHAWpPzuaDeTskXGl1Vb2ZpRb5c6rzPE3Knb40b85KNC1L\nP3agtAZjmrBAEORjRdzZ9Xo9AKmZmQCowNuEt+PlSwxUFgAANNHRCvPTp1mgdawPCgUAAMqT\n9+zWzYcv3mQV2lwIyRfLNaFR8WWr1a5ZRh/4CcD92C4u/XHjkUxEAfC9yXLZ7VkUpBHQPf0d\neF4asV2Jrq8ryTonsLodRqYnbX36knwkt2f4oJa6DnSXUwT0TUb+gvXCuMjQ+ePFpUuwagcV\nBEEfq4hgp2rctCr39OpJS9psGVk7rES1amr0yO7f8nv0CeGgDy7esIEopW+WQDmf75w5btam\nc28c7/giV1Gy2VdTfpwzuJYuUMfrCAfhvG/TD4+kuxCvu+1BDjld87Xq9lJWJw9vSDRgPY8Y\ng6XcUdVZvZP9j8Jj+3O3agRBcxOWh4t9cHbOp8MNZuuB0/bzNwQRIaFzxsJWJhAEFamo20TJ\nb+YOWNNxy+S60fePYHta9u0VvmX9oCrVd9TSpV05+1Jcf2RLrfeLdN+Z1bjx3Psevjq+drtG\n9aqWCNFqNEoxwDxOc17Wm8Q7F8+dX/vN+SOnt1zZNyA+IO98SJKTQklFQw3dhXjdLQQpJRB0\nkQX+2KQvpVnx1fcd59ORcjrBprZaETsm9P8/ClBbMldfM51vEtSmT8QQPsev7xa4wZw/fw3l\nQYKG9lS0rA8H6iAI+hBF3tfU7Tfdu91s095rmkgApM0X7Jn7uuecc6ePAaCs/M22bcN90O0k\nde3I+ff5tSafOTivVeQ7p1wp66ONAzsOPzRs2LY2ZweHeL8kmnCl/tuCoVg8RtFzbg88ZKLY\nLbtjf5CPja4ubxcvVgjZmw8uG89cN13oGzG0ma4t52MbDvkWhWGG1TtImyNswSR+qI7uciAI\nYowP+MDK1dfsN71mv7f/oWn0/dmsCblvMhF9iVi1T56/xj9O3yPDxiz5V6vIf5po5aiqfLvz\n50uh3fYe/N02+OsAbJCBZiOAy+Hw/fpR9Jkeo2ivfAOfw5mngcN1xeZCOrL8rv25AVvQWNWz\nLNt/sCfyDzTQNm+ua0d3IUWgCNKy/xSSnBY89VuY6iAI+ihFBLusy5uPPBXX6tO31v/MuPJk\nYaV82OnJarUCoAsJKWL5nKxkyVAACgsLAQjAYOd6ZJNWlHNEgbqGENxF0HlmS7yAfyI0mO5a\nAkeyCf/uskUr4W1pp20UFfgbjN7vTOFRE2ZoEtSa7kKKZly3y3H5jrr7F5JKpemuBYIghiki\nKHAebR09esq+JN8U825RCQlikHhwzxP0fa/Cnx49mQrEJUtG+Koun3I9sovLB+yCdytJTjKa\nZRzuNDU8E6nY3M5B+58w6qS8Na3UMNUdz9+/L2dLc127WGlJumt5H9xgtuw/6bh0Wzugi7pH\nW7rLgSCIeYoIdhEdetQT55w6dNvjm3LeRdBuzMiS5IM5zRp9u/zY/UwH8dcvk86cp2fWjWrS\nbPYDKmbI8PYMOC2eIqmPXd6DZnikVRTeKYdmFADTTBaUouZoVQ1g47pi8uMNW59jRr2Ut7yF\nOlbl11sEfOCPwmPH8vd1CevXJ2KIPy+tsx76I2fiT5bfTinaNFK0aUR3ORAEMVJRd/zYYbt2\nPG07qGMrfP73/ZuUDVP87RsEcl2Q3MuPDUGtn87sNrQbvG3j+E4bx3PFmvCocJ1CKuAgDpvN\nlJuZ7yAAAOKS3TceWdKIEcGAAMLIjwiguAHFchCePDB3TpxyuS+5PVv0QQnwkInP5sGp3166\nL2Z4Lmcg0+ooh1ZhxTkl72HBTKcKDp83/l5f0+wL/Zf+meooDPc8TbIev+B5mqRo3VDTrxNX\nwoAPqBAE+aciMtmzuVUrznkOAADLv2m1/B0vKD/r6bPZXu+BLijRa+vT5iP3bdh86OzVG/de\nJj/P+vdXOEJ1VJUWjdp0Gzisf/MYBjU++5jFcoUbswEHqDr4b1v8T4ZS1EyTpYpQWAeO1RWH\njY+cq+7bm0SL5jZU9SrH9q0SbsK1MGWmh3B3COnRLrgbj+OPH408T5PMu48jbzIEIbrQWWPE\nFRPorgiCIGYrItipK3zRs+f7cltUBXWx1vPP+PqafWfW7DsTAEBiTqvZ4sS4YrlGqxIH7IaC\n/zDtywvqE8bXBOCA1mSjmccBy3WB35/PBzY8dKy4Zx9SWTa9bgDuH/pYaa7Xu3J+ceC22Qk/\n++1ZYaTDVbB0M1+vDZ0zVlwmnu5yIAgKBEUEu8hui/d2800lH4ErkGmCZezJAmiWR9kyiO4q\nit8zFLvoQeZqVCE8fxxKYZY9ia5ld2Gq+7eLxtM7szYo+KqRsVP9NtURZmv2hAUUgunHDxKE\nB277TQiCfIvtq6r9H+kkAE6BgOtgV0AQ35ks5QQCeHTY57uRjcy8Yu1ZVjq1DttTHUkR18wX\njubtbar7ol/EN3SX8w8oyn7+hvW3UxyBIHL1bK4M/glAEFRsYLCjAYVT3A+eQEZS3RRBiUsE\n2q3/O5MllyD2BOv48KCkz3MhHZl7zdooSjS/kYrL+p/lLxnL71iuVVPV+TK0D921vBvp9hjX\n7nLdeSKtV1XdtQ1MdRAEFS8Y7GhA4aSk8of2LsFyEACAICyg9hYgFHUbQedoVPHwUPPPk2zC\nh50x1Q4TfV9fCVOdES28bbk6LGZSLXUDumt5BzzPULhyK55vpDBcP2mItGZFuiuCICgAwccq\nPbgffIZE3uI0SSVFgJ05scpq5wEAu9Z9vrUPHWW0gl/baQTsjnXZnozblqsXDCclPGllZQ26\ny/k7CsM8ia9Nm38jXW5V55ayRjV5qsBsSwlBEO1gsPNrnhdOxy1LyYNV6C6kOO1yODfbHWNV\nCj3cM/F57uehx5Pd8xupWJ7qtmSuvmo6xwGcbmH962mbiLj+1QSOwgnj+r2OK3d4amXI96OE\nMYF5Og4EQX4CBju/hqS5AQCK5toiX8kUOEVtsDn6yGXDlHDE4rMgBLXtqTNYxmN5v7oH1ttX\nTecGRI6oo2nkb5EOAEAhaNbI2YTdoRvRV960Dt3lQBAU+D482JGOvDdvMg12fnj1qmFcVCAU\nerEsCABAYZRpf56kvJzDC5zxmLNuj4EgBijYfiLC5zuZ4jn9xrOmFXva/vwFQnoS7Y9vWa7c\ns9yopKzeKKilH54qQRGEYf0eCkHDF04RxkbSXQ4EQazwISu3nI+3jWmVoFWHlapcq26DQduz\nwPlhMQldF183eb08VjMfzLccLggZG0N3IcVpn8NVSSiM5sOh4s+SasF/vmsvqeG3jPO7MSrf\nWJgyc036wnRXyuDoMWNiZ/hhqgMAGNfvcd16qB8/CKY6CIJ8psjnK/Fscav6U244JVG1O3RQ\nJ+87AwAAISUjCmdOafoi//y9JQ1ZPQ/kTdaTBlktlbZ3KN2FFJurHuQegizQsnSQqRj9fNfO\n5YANbQJnjv6j/Ja7Ld2VMjpuehVlLbpreTcKJ8y7jjou3dYO+FJSrTzd5UAQxCJFjdgVbBk3\n8waoNfVyWtqtYztG1X47/1p1xq0Hq1pKXiybtCHd+zUGHqrol+BGzHKiUNsnzPvV+AgJwHST\nuapI2A427vo8mXbiYgYysKIsSsm63ScZ7tTlqfNOFxzpHNq7vMJPNxURZmv2qNm2ExcVrRrK\nW9SnuxwIgtiliGBnPXHoAhrxzc8LGgX/9ZX8uBFzhkRQd86et3mxugBFERQ/qIiDXz3JTgol\n1R389DSkT5CHE0aCnKxmXxgpbsvv2kOkvL7lWTdWbsXMK1LnG9HCUbHTOoT0EHD8dJ2v/Y9r\npNsTuWpW0NAeXNjTB4Ig3ypiKrYgP58C0bGx78h/nBIl4gDIz88HgO2nGH0CrrSIeEM6ScAB\nReY/BjngdOl43ATB/7F3l4FRXG3fwM+6ZyUbF0JwCe7u7m6FUqS0RYoVaJFCW0rRYi3u7u4u\nwaVYgBCI6ybrMrsj74f7fu+npSEJYXdnZnP9PrXJZuaKkPnnyHV85zPyPgNGTrxguJGK/dik\nxLU4MeL6NcmLCYqYFD1HLWDu0cnGIxcM+0+rBnTmB2vprgUAUBIVMmIXEhnJR89jY/MZlqPi\n4xMQR6tl7m9YVjMezxFF+c6UpZkk91ms9UUiMRwg9gl2v7A9zHKuaKseWMJanJhx05+Ji9Ic\nKWOjpjM21dkfx6VP+VW/65iyV3tV7w50lwMAKKEKCXbyTgO7Kk17xw38/a6O/NvbCV3srKnr\nM0TNenYqocu3PY20E/ImKrqrcJuFBpODosZDt/1PYMepAy/tvStIO0aLS9RonZ2wLXk7J82R\nPC5qRllZRbrLyQ9F2Z+8yl23hysWB80Yo+rfGcEfMAAAmhS2K1bdb/maQ3cH753YIHpZrbpB\nOgyZD47vcvrltVvvzPKmi1eOgCbqnkERFMdXnt56kjxis09RKqDLSbG9zsO/OafPtBKDStJY\nHUmRN/WXtqeuIRH5U/kVIWImNg0hrbas+WuwV29F5aK044fyAxk6oAgAKCEKf9BGDNh1L6j2\nlKmL9z24lIwQQo9Pn0TiiOZjV636bWhVWDDlIdY7Rk1/H2l0kkeQOEW1kvjOzLKXZVmJgcdy\ng2W843200aoSFI6PZO46m3OsjqpR7+DP/IVM3EjkSs/K23LIlZoZsmCqqKxPtZwEALBUUR4S\n3JCWU3fen7w29fmT+AwzLlKFVahWKVjiI8NJdCAQKnA0jjDi2Du7z0zF7rNaZRyOhleUbtjg\nfW/0+ICjuVI+Z1sXjb+kBH0Nd6Stvaw70zd0WIeAHnTXkj9nYlrWT6s4EpFmRF9IdQAAhigk\n2L3b8/2fugZD+nesFiCQh8c0Co/xTlm+jSIpYURBBwbgOidCSBTtC5NuOQSx22LrLpXIYNXR\nx3OR1ORLBq2Uu72Lf8lJdSRFXtCduKQ73S2of/uA7nSXkw8KJ5yJqXmbD/JUfoEzxvC10HMb\nAMAUhTwqrC+PLRrXvXpoSLUuX/+2+2aKzTtVlQAFhhxnisNnep3ss9rEHM50tZLuQtjnSbar\n16Hc13n4H+3UAdISkeooRL22vlid9Nue9E3N/dt1Dx7AwLPCsDdJ6VN+zZi+iNAbVQO7QKoD\nADBKISN25Uau2y7efeDgobMn/5x+8s8Z8tLNeg0eMnhwn9YVVdBntnhwCiEkCCiot2re/ixB\nsIgrY/2X+JLdsd5k+UIhh+G6YphyySDkcXZ01ZScdXWbUlbezLukEWgnRs+OUdSiu5x/oSjD\n/tOGfaeEkaGhi6YLo8Jg9ysAgGkKGQYQhTcaMn3lkXupOYk39yyZ2DuGvL/951HtKwWH1+k9\ncdnhB5lO75TpQyiCQgjxAwsKdvbHZu3wUG9V5EFLjabGYtE30OXkIxkxcu4N0zsjPq2BonYw\nQ89XcC+MdJzPOR6bd3lk5ITFlTcwM9Xlrttr2HdK0b5Z6NLvhaXDIdUBABioiPM7HHmpRv0n\nLd0fm5iTcvfgiu96lzdcWDGpV53wxr+99myBvodCCCG+pqBpVpfOKSzF+j2kP+mNCS58lJ+c\n9QOP3nUywdF0R/a+l7Yp9RQNw0rEgVQXdCfGPRuyP2NrS23HBqpmdJeTv7zNB8yXYv1H9vMf\n1Y/uWgAA4IM+eopHpAwMDgkLj4wMkL81mQi7Hcbs3AzXu3Cdi6dg9+zbS5drj8U6W62sISwR\nA07ukmDAJ5zXdykr+b6RX2AJWFdHUsT2tLVXc8+1C+jWObCPgs/E8wlJqy37t3WOuATtV4Pk\nrRrSXQ4AABSkqOnBkfn44vGjR44cOX7xcRaGEE9ZvsWwOYMGDe5d2aP1lUBEnovCSFltJj7h\nim6e3lhRKOgj84WNvV5zN8M54mReqII3u7GfpgTsgdU5s/amb3lgvNUhoEe/0M/pLid/WEJy\n9m9rKcwZ/ON4cZVydJcDAACFKCTYYSk39u3af/To0TO3k6wUQkgcVrf3pEGDBg3oXDu4REwS\n0YbNq3f2WqzPna4FGpUAFiEV2XOd68frxiAZ72gfrUzg+1+3WP2VTSkrFDzllDLzKsur0V1O\nPvDsXMfz+Lxth0VlIrXjh/H85HRXBAAAhSsk2MVvHDN07nOEeOpK7QYOHDhoUK/mZfx8fySB\nVo5XNsTlcP3YOhX7AHPO1Ru7SiVtJAX16gPvWf3AYsOpX5opfT7VUYi6lnt+Z9r6Gn71voma\nxsCGJgghyunKnLMczzWIq5TVjhsKqQ4AwBaFpAdRSL3+U74cNKh/x5qBvtBUjQ1cmZiolJjH\n2i0HeyzWaAH/N39o7lVUFEJrHlnOJzpmNfZrHO7jA+FGl/73dz+nON7VUzX9LOxLZqY6RFEZ\nPywh8oxhS2YIIkLorgYAAD5CPsGOsBn0NpwnVaml/OjPlq6y4Qgho06X/8dL1SopWyMIM5mv\n6vkFdrljstcu12mbfa7GRw5D847l98wrH1iGVpV9VlVGdy0etyt9g86ZNbvckkhJabpr+SBX\nRo7zXWrw3AmQ6gAArJPPtGrcwiYBAQF15z3+338XoMnCOK/X7OOcqQ6/Nv50V1FMvxpMFYWC\nrlLW92rxGgqhC4nYlzXlc5r4MXLwyp1u66/dM9z8LHwMk1MdQihv036+Vi0sE0l3IQAA8NHy\nGbHzK9+8c+eo0Eqq//13AR9fqjy7N28yE0fIykf8K5frAeb8Sa0Uwp6JIlt21/wy1zWpno/3\ncKYQdddwY0/6prKyirWUDegu54Ocb1N0f+xwJqVrxw3lin18WhwA4JPyCXaRg1afGJTPfwPv\nIK0EM9cdFYxCaJPJEsnndYEWJ0Wmd5CHX9s/qyprVcqXM0SC9dXBzO2vLM+b+bdt6d+Rz2Hi\nxiBcpzefvmo6c01UOiJw8ghp/ep0VwQAAMVRyG9Y3JKrs/LVQcp8HjukLS/bxFMFK2Hvo1vh\nOpcwjGVfUwqh342mEzb7bLUSVlwW3cVER56DHFrVl6PwO1v8isRfNIKA6WXnl5NVoruc/GFv\nkrIXrqdcLlWfDn5dWnIEsFUMAMBWhbQuebm4eUipb87n+z7Djj4hId3WZ3igqpKLMOGE0cUV\ns6ylzF0MW2eyfOWn6C/3/eX/7nItBVt+39IkXFRaxcQRLLe4qDv5U/xUDuJ+FTWVmakOz8nL\nWb4lY/oinkoRtvR7Zc92kOoAAKyW/xMl7+7uXXdzEUIZd/MQ8frkqlWJ77+Esj3ZcQ+hqk44\nUsydnCkO0k7K6irpLuTj/IW5gnm8sUofXyjmRnoHOfq0vnG4cGYjX16lejn3TG1lw2+iptFd\nSP6whOSsOcu5fvLAaaMlNatw+DDcDABgvfyDXfqpX8bNff7//y9jzbh7+X+0uFaP9hEeqauk\nMp3P5WuFPH82jRmQCO22WBvBSvMiM2HkuPN6mZCzsq1a6qPtiP9zCGyGI3VI2Gi6a8kfYbbo\nVm3nhwSE/DyJI2JrgyEAAHhP/sEuoteC7WUNCKHUQzNmnIicvOmrGu+/hMOXBVZq2Lx6MMsm\nDRmO0OPSGgp2TcXaKSqTIHrBnomiiU3DxpzRS/ictR18ONWR65KXPTTeGV1qUkV5DN3l/AtF\nmc9e1+85wREKAqeMhFQHAPAl+Qc7ZbUuQ6ohhNBbx+kjueV6DhnS2KtVlWysetY7Kap3Zo6a\nyw2HaawiSDYRX5zUNwwTLm+j8hOxKb4XnRHX703fcs9w8+uo72orG9JdTj4sl2/nbtin6NBM\n1a8TnBUGAPAxhZw8UWrQ6hM9cKT7wLkTcPKEu2Hv7HSX8BFcFDUyJzeDIA4HBQTx4MegEBRC\nc64bBVy0sZOGy6r4XnR2wrY9dU28Ne6z8C+Zmeqstx7p/tgpb93Qf2Q/umsBAAD3yyfYxS1s\nEjP3eZlp994sqPOf/y7g46vMefrsx6oeK6/EMV/XB0+JoruKorqFYfcw52y1Mlrgs/s63Wj9\nY8u1FOzHJkqfTHUUos5kHzmdc9hFOoeEjW6saUV3Re+jnC79ruOmE5dkTetovxpMdzkAAOAR\ncPIEg1AYieuc4oqs6Rhy2GqvIRT2gxYnRXA9BVt42zyquuwzX+xa5ySxpW/nxlvjmvu37x0y\nRMZj2PwmRTmexeeu3Y3n6lUDuih7tqW7IAAA8BQ4eYJBnOkYopAwlB3bSx9gzvM2+1yNCqZg\nC2XDqeX3LTWDhdMb+tofQhjpOJCx/bb+qoO0zyy3sLS0HN0VvY+0O3KWbbY/fC6OKR8w6Qth\nNGzkBwD4so+fQaNsqX/dj7eoK9aJCWHZ+QhMR2EkQoivZUGvExKhw1abhsfrCZthi+BxlvNR\nlvNIby3dhbjZS8uztclLnCTWXNOutbazvzCA7or+wZWaadh70nr3Lw6XFzhttLRODIJTjAEA\nvq4IwU53a/n0mev1/c4f/DKEeruxR9Mvj6UTCPGDWsw+cGhWE7XniywpnCkOhBDis+DZ8xfm\nPGS1/aBW+ubGTrc68tq+47m1tJIfE8CCyF50l3PPHMrYESUtOzhsVLAojO5y/okkTaeuGPaf\n4UpE/qP6S+tVh92vAIASorBgRz6f37HVD/dRyIAvBAg5Ts6bcixdUffzr1tT59Ztnd1rQu13\n2zrBCis3wRJsorJSvpoFj/8rDoeIwxkMq+sKk2Ymplwy1AsVjqvjO1+rBNurcznH7hluNlQ3\n7x863I+voruif8AzddkL1zmT0xUdmqkHd+NKYGYBAFCCFBLsiIsrltx3xXx/694vdUWIOHnw\nqIHbeOWRzWND0bTajvC+e7edXt+pDzvWhDGf/YWVFQvsknF8l8U6VOE7ScVDMq3EV2f1EX68\ndR00ciELBmKLIhvL2J661oKbRkdOqqtqzOMwa40lrtOnT1/I4fNCF08XRoXTXQ4AAHhbIcEu\n9cmTPFRlyud1RQgh9OjyZQOq2aVLKEII+bVuXRftTUhIRaiM5+ssEezPLPJGzBr8+DcCoe1m\nq5NCQ+Uwt1WQ+Dx81Jk8ikK/tVD5RqojKfJy7uk96ZvkPL/PI76p7leH7oreh71+l7dxP1cq\nCVkwFeZeAQAlUyHBjsPhIKRW/2cdXcr160moVJ8WUf95n91uR4iiKM8WWGJQTtL2lznwK6Zv\n2dtptu6yWKeq/Px5sL7ug0gKbXxidRFoVzdNKaUvNPmz4OYtqaseGu+0D+jeM3iQkMu4oWXT\nsYv6nccE4cGaYT0h1QEASqxCHjnh5ctL0bEbN0xjeogfr996D2lGta/7n3dlnjv/FAnaRzFs\n0TRrUS6KwkhRGQndhRQiFsPaSiWfK+DB+UE4iaZdMRx5bV/QQukbqS7HmbUxecVb2+uRkRMa\nqVvSXU4+9NuPGI9dVPZspx7QGXHhTw4AQMlVyFOH22HsV2W3Lhlc9WVV8Zt78VTk2KEteMj4\nePfKZb8tOmFR9h7QgelBBLjXI8w5VeVrzdjcKMGAT7tseJLjWtRS1auCL/zrwCl8c8qqNEfS\n1DLzyskq0V1OPvI27jedvqoZ2tOvW2u6awEAAJoV9qctv85Phzd+XsX59G68LajpnO0/NRYg\nlHJk7qxtr/y7Ljixtg/Tl4QBd8IoykZRgXAsbH4wghp9Wt/jgM7goPb30PpGqsNIx59Ji5Lt\nb8dGzWBmqtNvO2w6c00NqQ4AABBCReljJ6n6xea7X2xw2EmRRPCfJeARAzfdGlSxVnmN0NPl\nAWaxkBROUaEQ7P6FoNCMK8YryY65TZXdyklkAl/YLfHYdG9X2vpcZ86E0j9UkFehu5x82O4+\nMR67qBnex69zC7prAQAARijqAiAez/H2/u2ETBMuUoeVq1avgcoXlg6Bj0EitNJkQgj5QmZx\nt41/WY7F2xe1UvUs7wsDdSRFbkhZflt/NUZRa3zpH8LFpeiu6H0UThj2HDdfiBWVLQWpDgAA\n/qco8Uwfu+ybMT/tfaon//9beJqqXb/5adH3PcpC6093IUw4QghxmZuanjqdey22SUq/KAGk\n+n/IsZFbntq6lJX4Rqqz4KbtaWvvG2IHhH7RRtuZy7BOdQgh0oGlT5pPGEzqId0lNZk4lAgA\nAHQp9AmNPfixbeu5D5yK6OZ9W8VEqvmW7MTn187f2S64SQAAIABJREFUPPJTz6s3ll8/P74K\n437rs5PtiQVxOaKyzD16NdGFa7jcUdBI4p9MGDnvptGOU8NifKFjs8GVtzBhlhHXj4ic0Ejd\ngu5y8kG5XFnzVpFWe+ii6YKwILrLAQAAZiks2KVunDj/Abfe9Gun5jf2/99gEmV9c2xa3wGr\np327pf/5EfCr1R2c72yiKDFPztycfN2BhfCZWx4t9A6y1yGdEaMm11PUDGLBWXCFWpu8BKdc\nM8stDBEx8dgGCnNm/rTKlZweNPMbSHUAAPBvheyK1Z85dsMVOPy3n/+W6hBCHFnZ7itWjQlz\nXD52zuLR+nwPRVAcTv7r1LgS5samdJw4abOP9lPQXQiDYAQ16aIhz0Hu7e4/pApzh1qLyIKb\nNqesem15MSB0BDNTHSLJvM0HnW+Sgn+aKKoYTXc1AADARIWM2OVkZ1OoTPny+QQObqVK5RGR\nlpaJUFnP1OajKIR4+cQ6ivz32xgERxRCqJrQFwal3MKGU5MvGm6mYft7aMtp2L3okEJUou3N\n9tQ1RtwwPGJsLWV9uit6H+XCbXefGPYcx3PytOOHCUszMncCAAADFPJACggM5KAn795RKPRf\nWSQ5ORmhcDgw1E1caQ6+hrmxyUAyO3h61+005y+3TIlGfFVbdfVA5n7Xiui+IfbPpEUagXZK\n9NwQMcMyE0maL8Qa9p0kjBZpnZiASSMg1QEAQAEKCXbqDl0bC86unzK738m5DTV/m7e1x62c\nviYBVRjSPNizBZYcFOIqGDoVG+d0fZ6dW0koCIAOdghlWYnPT+ZFqXj7e/hX9Gd9qkMIPTU/\nLCOtMK3sL3wOs4YeKReevXiD/cEzebO6qoFd+QEauisCAACmK+z3ePio32dvaz7r58aRO1v2\n7tm0SqkAkS0r4eHJPYcf5pCRn2+eEOOVMgGtTtvtEg5nZ6AWYh1C6MBLO0FRe7v7K0XsPpPU\nSlheWp6+tr6I1V8eHj6WaakOIZS7ZrfjycvAqaOk9avTXQsAALBDob/KhbVnnruqnTxmzrZL\n25Ze+t+bxeGtpqzYOL+r2qPVlSSWO0ZxBSb2y9CT5G6Lta9MJuEwt8ee1+x6YVt2zzy+joLt\nqS7Dkfrzm+9cpMuPr+wVPLixphXdFb3PdOqq5eod7bjPINUBAEDRFeVvdGXtMRvuffHby7ux\nj95kGp18VWj52o3rl1Mz7u97VnO8tAZ8ybjFQ2dt9nl6owBxvoL2dQi90eNL75r7VZJ+U4v1\nX437xliE0LIqm2U8Jn4u5vM3DftOyprWlTdn3E4OAABgsqKGMwKz2XCuSKoM8FcGRkSGKCHV\nuZPjtZUw4mKGdSfOJciJufpWEvFMtVLBZfcA1ad7o8e/OJUX4cf7vqEfj+VfjC0pq2P1V9oH\ndGdmqkMIWS7fEkVH+I/sS3chAADAMkXIZ9jb/d+PmvzHpRTH3z5MW2vAtCVLJrcIhNk5d6Aw\nCiEkimZWsMsiCAqhGSplcInfM5FiJvoc1kUp+avbqeVCdv/QPzbdu5Z3vmtQv06BveiuJX+u\nlAwsPkk7bihXxqx/EQAAwHyFBrvMvZ81Gbg/gxdYo/tnbWtFawW27JSEh6cPX94xtd2d5FMP\nV7Rh6J/84JP9YTKXEfCD4bQJhLY9tfK5nLUd1EEydn817hiub0xeEaOo1S2oP495h8AihCiC\nzFm2WRCslTetQ3ctAADAPoUEO/Lmb5P2Z6haLrx8bGr1vyU4PPvqrK6dF6z+9vcxz2ZW9myJ\ngBapOHHTgc1SK5n48PciO059e8FwMdExsLKU7anuku7UocyddVSNRkSMZ2aqI4zmjO9+w/OM\nwXMnINisAwAAH6+QtUJJsbHpKHLkginV/zkuxw9sPn/FV5Hk8yvXdB6srsRwZTs5PA5HwJQn\nmZkkR+TkanjcJmIR3bXQbOUDy9VkbGlr1Y9NlHTXUnwW3LQ7feOOtHXV/eoMCRvNzFRHWmzZ\n8/+kCCJ85RxxZTjPBgAAiqOQETupVIpQcEhIPoGDExkZjpDdbvdMYSULZSe4Mh6XMQNCP+QZ\n0glif5A2sGSvrksxE5v+sk6oK+9WTkJ3LcWX5khelDALIU6/kGEdAnvSXU7+SKs99Zs5lBMP\n+XUKP1hLdzkAAMBWhYzYBXXsWpf37NKl7H+/y3Tz5lMU1aRJmGcKA7RxUtQ1BzZbrawo8IVj\nFYrNhlN/PLDIBJxR1Vm8jjQby1icMEcj0M6rsJyxqQ4hZL1xn7TaQ5d9L4yCXykAAFB8hbVt\niP5m7a+1b4xtN3rd5bdG/L9vxPXPj8zq9tXRyHFrptdleeMH8C93MSdGUU1L/CTs8BN5+17a\nhsZI+az9Gccp/M+kxSKuaGzpGX585k4lOxNT87YcVHZvIwgOoLsWAABgt0KmYuNX9Oy7NhE5\nUtZ/2Wr9VxJNcJBaTBgz03U2AiGRct+wSvv+78UVp1y9MqWCZ+sFnnfebq8mFJbwFid74mwP\nMp3LWqu6snYS9oHx1rqkZQQipkbP0wiYO7npTE7PXbOb569SDepGdy0AAMB6hbU74fL5fGlQ\nmQpBf3ubf0RZ//xe6ydm7cgG3bAUB1fBlCCV4MJriEruJCxGUBMuGM6/c7QuJe5YRsyU/Swf\nKc+lW5O0uLK8+qCwkUGiULrL+SBHXEL2gjV8f3XQjK84bO/7DAAADFBIsCs39tjLsd6ppERz\nJjkkjDkoNhknOkvZOkz16ZbcMV9Lxla0VXUuw9YvAoWotUlLKESNKTVFwmNuj1/zhZv6rYcF\nYUHBcydwREK6ywEAAF8AJ4MxBUfKlBE7A0mG80viDwZGUEde27c+s35bV8HeVPfa+uJgxvZ4\na9yU6LnMTXUUlbtxv/nsdUXrRurB3SDVAQCAu5TE5zcowAuny0VRmhJ2MixJoZ3PbRufWNIt\nROcykmExTBk9/Vj3jbFrk5aUkVaYWmZeJXk1usv5IPP5m5YLN9WDuym7t4FGxAAA4EYQ7MA/\nvHa5/LncysKStcbuQqLjp1hjj3KSsbUVkX5MGTr9WOd1x/ekbaqvbjY6ciLdtRSEdGDGYxdk\njWsre7SluxYAAPA1EOzAP1yyO0L5vBI1hKKzkwtum8urBQtbquiupfgOZe48kbW/c2Cf3iFD\n6K6lINabD/S7jpNmq1+31nTXAgAAPqhkzbiBgr3D8fuYs5uMqQuzPOPcO0eSEf+pmR/dhRTf\nXcONU9mHWvp3YHiqc7xMyF23h++vDvllkrAUNCIGAAD3gxE78H+WGEx8DqeWsAStZL+Wgs27\nYRpaVVYziJWftYty7k/fdjn3dGN1y4FhI+gupyDYm6ScxRsEYcEBk4bzVCyO0QAAwGRFD3ak\nJfPt2xSdmR9au2YI1ykoSU//EiGTIC7ZHbPUypKzwO6dAR99Wt8wTDizEftyxkvLszuGa+mO\nlHhrXPegAZ2D+vA5zP07zZmYljFjsSAkIGDCMEh1AADgOUV5Elj/2jpj6i/bLsUbCYRQ9Z/i\nH9eZX2q8cdLm9VMbazxdIPAWA0lSCLWRiOkuxEty7eR3V4xBMu4f7dXs6oyb5ki+Y7h+MutA\nmDgyWlq+c2Dvan516C6qIDnLNttuPxZGhYUs+A66EAMAgEcVGuyIZ4vaNf4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2Gv2uY5ZLtzg8nnbcZzwVC85hAwAAUIAPBTv9toGltxXh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\nWINMherEOY9BfYUerrYuDgAAAByYI0yeELf9fPdvOf3Gr17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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "x <- runif(10^4)\n", "for(i in seq(-1, 2, length.out = 10)) {\n", " p <- prob.true(x, 10^i)\n", " y <- p > runif(10^4)\n", " ROCR.pred <- prediction(p, y)\n", " cat(c(\"AUC(b = \", 10^i, \") = \", performance(ROCR.pred, 'auc')@y.values[[1]], \"\\n\"))\n", " plot(performance(ROCR.pred, 'tpr', 'fpr'), add = i != -1, col = 3*(i + 1))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "To finish this section you can move over to the\n", + "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1094727).\n", + "\n", "## Logistic Regression, Linear and Quadratic Discriminant Analysis" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "We will run logistic regression on an artificially generated data set with two\n", "input variables." ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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PEaOyINU6bM230rCklKkv+MASJSK/v2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\ntOQGBqIzSFhAQMC8efMCAgLatWsnOksp09KCnZ3oEERERKVBrYqdIuPprYu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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "set.seed(321)\n", "prob.true <- function(x, a = -1, b = 10, c = -8) { 1 / (1 + exp(-a - b * x$X1 - c*x$X2)) }\n", "data.train <- data.frame(X1 = runif(100), X2 = runif(100))\n", "data.train$Y <- prob.true(data.train) > runif(100) # add column Y to data.train\n", "plot(data.train[data.train$Y, c(\"X1\", \"X2\")], col = 'blue', xlim = c(0, 1), ylim = c(0, 1))\n", "points(data.train[!data.train$Y, c(\"X1\", \"X2\")], col = 'red')\n", "boundary.from.params <- function(p) c(-p[1]/p[3], -p[2]/p[3]) # intercept and slope\n", "abline(boundary.from.params(c(-1, 10, -8)), lty = 2) # Bayes decision boundary" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we use the function `glm` with keyword argument `family = 'binomial'` to fit\n", "the training data." ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/plain": [ "\n", "Call: glm(formula = Y ~ X1 + X2, family = \"binomial\", data = data.train)\n", "\n", "Coefficients:\n", "(Intercept) X1 X2 \n", " -0.6273 6.2940 -5.4954 \n", "\n", "Degrees of Freedom: 99 Total (i.e. Null); 97 Residual\n", "Null Deviance:\t 138.6 \n", "Residual Deviance: 78.78 \tAIC: 84.78" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fit <- glm(Y ~ X1 + X2, data = data.train, family = 'binomial')\n", "fit" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The formula says that `X1` and `X2` are predictors and `Y` is the response.\n", "The data is taken from the corresponding columns in `data.train`.\n", "The `Coefficients` returned by the fit are $\\beta_0 = -0.6273$ (Intercept),\n", "$\\beta_1 = 6.2940$ (X1) and $\\beta_2 = -5.4954$ (X2). As you can see, they are\n", "somewhat close to the parameters we used to generate the data, i.e. $\\beta_0 =\n", "-1$, $\\beta_1 = 10$ and $\\beta_2 = -8$.\n", "\n", "You may want to play around a bit with different values for the size of the\n", "training set and different values for `a`, `b`, `c` and the random seeds in the\n", "data generation process and see how the fitted parameters vary.\n", "\n", "The fit can also be used to make predictions on a test set." ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "data.test <- data.frame(X1 = runif(10^4), X2 = runif(10^4))\n", "y.prob.true <- prob.true(data.test)\n", "data.test$Y <- y.prob.true > runif(10^4)\n", "y.prob.fitted <- predict(fit, data.test, type = \"response\")" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The `predict` function takes as arguments the `fit` and the test input as a data\n", "frame with the same column name (`X` here) as was used for the input in `data =\n", "data.frame(X = x, Y = y)` in the fit. The argument `type = \"response\"` makes the\n", "predict function return probabilities.\n", "\n", "We can use now the predicted class probabilities to compute the AUC and plot the\n", "ROC curve." ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1]]\n", "[1] 0.9454462\n", "\n", "[[1]]\n", "[1] 0.9460407\n", "\n" ] }, { "data": { "image/png": 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0U6fvzx0NGj1Y4DAACumFaKXcUM3rXb9KrdRu0Y+vDxgw+OP3du86RJtDoAADRK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\ntJTUrHyjxdPP38fiBD8nAwAAVD3nK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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "ROCR.pred.fitted <- prediction(y.prob.fitted, data.test$Y)\n", "ROCR.pred.true <- prediction(y.prob.true, data.test$Y)\n", "plot(performance(ROCR.pred.fitted, 'tpr', 'fpr'))\n", "plot(performance(ROCR.pred.true, 'tpr', 'fpr'), add = TRUE, col = 'red')\n", "print(performance(ROCR.pred.fitted, 'auc')@y.values)\n", "print(performance(ROCR.pred.true, 'auc')@y.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that the ROC curves are almost indistinguishable and the AUC of the\n", "fitted classifier is alsmost as high as the one of the data generating\n", "classifier." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us now fit linear and quadratic discriminant analysis to our training set.\n", "The functions `lda` and `qda` can be found in the library `MASS`." ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1]]\n", "[1] 0.946042\n", "\n" ] } ], "source": [ "library(MASS)\n", "lda.fit <- lda(Y ~ X1 + X2, data = data.train, method = \"moment\")\n", "lda.predict <- predict(lda.fit, data.test)\n", "ROCR.pred.lda <- prediction(lda.predict$posterior[,2], data.test$Y)\n", "print(performance(ROCR.pred.lda, 'auc')@y.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `predict` function for an LDA fit returns predicted classes and\n", "probabilities for the different classes. We extract the probabilities for class\n", "label `TRUE` with `lda.predict$posterior[,2]`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "For QDA we do the same." ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1]]\n", "[1] 0.9458032\n", "\n" ] } ], "source": [ "qda.fit <- qda(Y ~ X1 + X2, data = data.train, method = \"moment\")\n", "qda.predict <- predict(qda.fit, data.test)\n", "ROCR.pred.qda <- prediction(qda.predict$posterior[,2], data.test$Y)\n", "print(performance(ROCR.pred.qda, 'auc')@y.values)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us now plot everything.\n", "For logistic regression we extract explicitely the parameters of the\n", "decision boundary, whereas for LDA and QDA we predict the probabilities of class label\n", "`TRUE` on a grid and plot the countour line for probability level 0.5." ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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rt27XJ2dn7y5EkV6e82/ycyMrJnz57u7u5//fWXULPLr+zsbA0NjRMnTnQU9rsC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\ndaIzZ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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(data.train[data.train$Y, c(\"X1\", \"X2\")], col = 'blue', xlim = c(0, 1), ylim = c(0, 1))\n", "points(data.train[!data.train$Y, c(\"X1\", \"X2\")], col = 'red')\n", "abline(boundary.from.params(c(-1, 10, -8)), lty = 2) # Bayes decision boundary\n", "abline(boundary.from.params(coefficients(fit)), col = \"darkgreen\") # logistic regression decision boundary\n", "grid <- expand.grid(X1 = seq(0, 1, length.out = 100), X2 = seq(0, 1, length.out = 100))\n", "lda.pred <- predict(lda.fit, grid)\n", "contour(seq(0, 1, length.out = 100), seq(0, 1, length.out = 100),\n", " matrix(lda.pred$posterior[,2], 100, 100), levels = c(0.5), add = T, col = \"blue\")\n", "qda.pred <- predict(qda.fit, grid)\n", "contour(seq(0, 1, length.out = 100), seq(0, 1, length.out = 100),\n", " matrix(qda.pred$posterior[,2], 100, 100), levels = c(0.5), add = T, col = \"orange\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "Once you feel ready, move over to the\n", + "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1094729).\n", + "\n", "## Exercises\n", "\n", "**Q1.** We revisit the bias-variance decomposition.\n", "\n", "(a) Provide a sketch of typical (squared) bias, variance, training error, test error, and Bayes (or irreducible) error curves, on a single plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent the amount of flexibility in the method, and the y-axis should represent the values for each curve. There should be five curves. Make sure to label each one." ] }, { "cell_type": "markdown", + "metadata": { + "lines_to_next_cell": 0 + }, + "source": [ + "(b) Explain why each of the five curves has the shape displayed in part (a).\n", + "\n", + "**Q2.** Suppose that we take a data set with mutually distinct inputs $x_i\\neq\n", + "x_j$ for $i\\neq j$, divide it into equally-sized training and test sets, and\n", + "then try out two different classification procedures. First we use logistic\n", + "regression and get an error rate of 20% on the training data and 30% on the test\n", + "data. Next we use 1-nearest neighbors (i.e. $K = 1$) and get an average error\n", + "rate (averaged over both test and training data sets) of 18%. Based on these\n", + "results, which method should we prefer to use for classification of new\n", + "observations? Why?\n", + "\n", + "**Q3.** Suppose we collect data for a group of students in a machine learning\n", + "class with variables $X_1 =$ hours studied, $X_2 =$ grade in statistics class,\n", + "and $Y =$ receive a 6 in the machine learning class. We fit a logistic\n", + "regression and produce estimated coefficients, $\\hat{\\beta}_0 = -6$,\n", + "$\\hat{\\beta}_1 = 0.025$, $\\hat{\\beta}_2 = 1$.\n", + "\n", + "(a) Estimate the probability that a student who studies for 75 hours and had a\n", + "4 in the statistics class gets a 6 in the machine class.\n", + "\n", + "(b) How many hours would the student in part (a) need to study to have a 50%\n", + "chance of getting an 6 in the class ?\n", + "\n", + "**Q4.** We will go back to the artifical two-dimensional data set in the section\n", + "where we studied kNN classification with the Bayes decision boundary\n", + "`bayes.boundary <- function(x) {(6*x - 9)^3/160 - (5*x - 12)/2.5}`.\n", + "\n", + "(a) Compute the training and test error for different values of `k` with kNN\n", + "classification. Plot training and test error as a function of `1/k` and include\n", + "as a dashed line an estimate of the Bayes Error.\n", + "\n", + "(b) Plot the ROC curve and the AUC for the value of `k` that lead to the lowest\n", + "test error in (a).\n", + "\n", + "(b) Fit logistic regression, LDA and QDA to the same artifical data and compute\n", + "the AUC.\n", + "\n", + "**Q5.** In this exercise we will perform binary classification on the life\n", + "expectancy dataset. We will try to predict whether the life expectancy is\n", + "higher than 70 years using the predictors GDP and BMI. You can load and\n", + "clean the data set with the following commands." + ] + }, + { + "cell_type": "code", + "execution_count": null, "metadata": {}, + "outputs": [], "source": [ - "(b) Explain why each of the five curves has the shape displayed in part (a)." + "data <- read.csv(file.path(\"..\", \"data\", \"life_expectancy.csv\"))\n", + "data <- na.omit(data[,c(\"GDP\", \"BMI\", \"LifeExpectancy\")])\n", + "data$LifeExpectancy70 <- data$LifeExpectancy > 70" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lines_to_next_cell": 0 + }, + "source": [ + "(a) Plot the dataset with different colours for the samples with life expectancy\n", + "larger than 70 than for those with life expectancy below 70.\n", + "\n", + "(b) Split the data set into a training and a test set.\n", + "\n", + "(c) Fit logistic regression to the training set and plot the decision boundary\n", + "together with the data. Hint: you may want to use the function\n", + "`boundary.from.params` that we defined above.\n", + "\n", + "(d) Compute the confusion matrix for the logistic regression from (c) and\n", + "decision threshold 0.4 on the training and the test set.\n", + "\n", + "(e) Fit LDA and QDA to the data, compute their AUC on the test set and compare\n", + "it to the AUC of logistic regression.\n", + "\n", + "(f) Group the life expectancy into decades with the following command" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "lines_to_next_cell": 0 + }, + "outputs": [], + "source": [ + "data$LifeExpectancyDecades <- as.factor(signif(data$LifeExpectancy, -1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Q3.** Compute the training and test error for different values of `k` and the\n", - "example above, where we used the kNN method on artificial 2-dimensional data.\n", - "Plot training and test error as a function of `1/k` and include as a dashed line\n", - "an estimate of the Bayes Error." + "Perform a linear discriminant analysis with `GDP` and `BMI` as predictors and\n", + "`LifeExpectancyDecades` as response on the full data set.\n", + "\n", + "(g) Which class would the LDA fit from (f) predict for GDP = 20000 and BMI = 22?" ] } ], "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": "4.0.2" } }, "nbformat": 4, "nbformat_minor": 4 }