diff --git a/src/lecture8.ipynb b/src/lecture8.ipynb index 90f96f3..a8f282e 100644 --- a/src/lecture8.ipynb +++ b/src/lecture8.ipynb @@ -1,1361 +1,1362 @@ { "cells": [ { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "# Lecture 8\n", "\n", "## The MNIST data set" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ - "WARNING: Some cells in this notebook take quite a bit of time to run and may even\n", - "crash the kernel when run on the EPFL servers. Therefore this notebook contains\n", - "the output cells of a run on a local machine.\n", + "WARNING: Some cells in this notebook take quite a bit of time to run and some\n", + "cells crash the kernel when run on the EPFL servers, because of memory\n", + "limitations. Therefore this notebook contains the output cells of a run on a local machine.\n", "\n", "Let us load the MNIST dataset and plot some examples of the training set." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "library(keras)\n", "mnist <- dataset_mnist() # loading the data set\n", "par(mfrow = c(4, 6), oma = c(0, 0, 0, 0),\n", " mar = c(.1, .1, .1, .1), pty=\"s\") # setting some parameters for plotting\n", "for (i in sample(1:60000, 24)) {\n", " image(t(mnist$train$x[i,28:1,]), col = gray.colors(256, rev = T), axes = FALSE)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "The inputs are loaded as 60'000 arrays of 28x28 pixels with values between 0 and 255." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1] 60000 28 28\n", "[1] 0\n", "[1] 255\n" ] } ], "source": [ "print(dim(mnist$train$x))\n", "print(min(mnist$train$x))\n", "print(max(mnist$train$x))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "To prepare for fitting with Linear Discriminant Analysis we transform the 28x28-\n", "dimensional arrays into 784-dimensional vectors, i.e. the training data is\n", "reshaped from 60'000x28x28 to 60'000x784. We also search for all pixels\n", "that have zero variance accross the whole dataset and exclude them. These are\n", "usually pixels at the borders of the images that are 0 for every input." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "X <- array_reshape(mnist$train$x, c(nrow(mnist$train$x), 28^2))\n", "idx.zero.var <- apply(X, 2, var) == 0 # identify pixels with 0 variance\n", "data.train <- data.frame(X[, !idx.zero.var]) # exclude those pixels\n", "data.train$Y <- mnist$train$y" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we load the MASS library and perform LDA. This will take quite of time,\n", "because the data is rather high-dimensional. If you have installed R on a\n", - "sufficiently powerful personal computer, I recommend you to run it there." + "sufficiently powerful personal computer, I recommend you to run it there.\n", + "(This cell does not run on the EPFL servers, because of memory limitations)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message in lda.default(x, grouping, ...):\n", "“variables are collinear”\n" ] } ], "source": [ "library(MASS)\n", "lda.fit <- lda(Y ~ ., data.train)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us prepare the test data in the similar way as the training data and plot\n", "the mis-classification table and the accuracy." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " \n", " 0 1 2 3 4 5 6 7 8 9\n", " 0 940 0 15 5 0 8 12 2 7 9\n", " 1 0 1096 32 5 12 8 8 30 27 7\n", " 2 1 4 816 25 6 4 11 15 8 1\n", " 3 4 3 34 883 0 44 0 9 27 13\n", " 4 2 2 21 4 888 12 25 22 20 63\n", " 5 13 2 5 25 4 735 29 2 53 6\n", " 6 9 3 37 3 7 15 857 0 10 0\n", " 7 1 0 9 16 2 10 0 864 6 37\n", " 8 9 25 57 29 10 38 16 4 790 12\n", " 9 1 0 6 15 53 18 0 80 26 861" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "0.873" ], "text/latex": [ "0.873" ], "text/markdown": [ "0.873" ], "text/plain": [ "[1] 0.873" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X.test <- array_reshape(mnist$test$x, c(nrow(mnist$test$x), 28^2))\n", "data.test <- data.frame(X.test[, !idx.zero.var])\n", "data.test$Y <- mnist$test$y\n", "p <- predict(lda.fit, data.test)\n", "table(p$class, data.test$Y)\n", "mean(data.test$Y == p$class) # accuracy" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Next, we repeat the same with multinomial regression.\n", "We set the argument `MaxNWts = 8000` to tell the function that it is allowed to\n", "build a model with at most 8000 weights. This cell will take even longer to\n", "evaluate, than the one before." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# weights: 7190 (6462 variable)\n", "initial value 138155.105580 \n", "iter 10 value 33282.974291\n", "iter 20 value 26173.678591\n", "iter 30 value 24672.543031\n", "iter 40 value 24229.953056\n", "iter 50 value 24010.800008\n", "iter 60 value 23932.917353\n", "iter 70 value 23882.106974\n", "iter 80 value 23818.241965\n", "iter 90 value 23749.036339\n", "iter 100 value 23697.758066\n", "final value 23697.758066 \n", "stopped after 100 iterations\n" ] }, { "data": { "text/html": [ "0.8976" ], "text/latex": [ "0.8976" ], "text/markdown": [ "0.8976" ], "text/plain": [ "[1] 0.8976" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " \n", "p2 0 1 2 3 4 5 6 7 8 9\n", " 0 920 0 7 9 0 11 5 4 5 3\n", " 1 0 1118 15 3 9 10 7 26 33 9\n", " 2 1 3 915 26 2 2 6 23 9 0\n", " 3 1 3 10 888 2 34 0 2 13 10\n", " 4 3 1 10 5 917 12 8 11 11 70\n", " 5 30 1 6 19 1 668 12 1 21 6\n", " 6 16 4 17 7 11 35 919 2 14 6\n", " 7 2 1 8 10 3 10 1 916 10 22\n", " 8 6 4 39 35 4 102 0 5 847 15\n", " 9 1 0 5 8 33 8 0 38 11 868" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(nnet)\n", "mn.fit <- multinom(Y ~ ., data.train, MaxNWts = 8000)\n", "p2 <- predict(mn.fit, data.test)\n", "mean(data.test$Y == p2)\n", "table(p2, data.test$Y)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we prepare our first feature representation. To have a similar situation as\n", "in the XOR-Problem, where all input data was around 0, we scale the data first\n", "to lie between 0 and 1 and then we subtract for each pixel the mean over the\n", - "entire training set, such that each transformed pixel has a value between -0.5\n", - "and +0.5. When we do feature engineering there are always many choices.\n", + "entire training set, such that each transformed pixel has a value between -1\n", + "and +1. When we do feature engineering there are always many choices.\n", "The exact scaling, for example, does not matter here. What matters is, that the\n", "784 dimensional vectors point in different directions, such that the pair-wise\n", "inner products are sometimes positive and sometimes negative and the relu\n", "non-linearity has an effect. If all inner products would be positive, the relu\n", "non-linearity would not have any effect and the feature representation would be\n", "a linear transformation of the original data. Linear feature transformation can\n", "be sometimes useful (we will discuss this towards the end of this course), but,\n", "for example, the XOR-problem could not be solved with a purely linear\n", "transformation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ - "X.p <- X/256\n", + "X.p <- X/255\n", "m.X.p <- colMeans(X.p)\n", "X.p <- sweep(X.p, 2, m.X.p) # subtract the means from all input points\n", "feature_vectors <- t(X.p[1:200,]) # we just pick the first 200 images as feature vectors\n", "relu <- function(x) ifelse(x > 0, x, 0)\n", "newdata <- data.frame(relu((X.p %*% feature_vectors))) # create the feature representation\n", "newdata$Y <- data.train$Y" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us run now multinomial regression on the feature representation.\n", "Note that we have less parameters now, because we went from 784 input dimensions\n", "to a feature representation with 200 features." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# weights: 2020 (1809 variable)\n", "initial value 138155.105580 \n", "iter 10 value 42283.013913\n", "iter 20 value 34453.953276\n", "iter 30 value 30854.088830\n", "iter 40 value 29663.308584\n", "iter 50 value 29000.061505\n", "iter 60 value 28470.259300\n", "iter 70 value 28123.439179\n", "iter 80 value 27927.197102\n", "iter 90 value 27807.099123\n", "iter 100 value 27725.248837\n", "final value 27725.248837 \n", "stopped after 100 iterations\n" ] } ], "source": [ "mn.features.fit <- multinom(Y ~ ., newdata, MaxNWts = 3000)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "To test the fit, we also need to transform the test data in the exact same way\n", "as the training data. Note that we subtract the pixel-wise means of the\n", "training data, because it would not be the same transformation, if we subtracted\n", "instead the means of the test data. Next we compute the feature representation\n", "of the test data and the predictions." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.9008" ], "text/latex": [ "0.9008" ], "text/markdown": [ "0.9008" ], "text/plain": [ "[1] 0.9008" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " \n", "p3 0 1 2 3 4 5 6 7 8 9\n", " 0 915 0 3 1 4 11 6 2 2 3\n", " 1 0 1119 16 7 6 0 3 17 5 8\n", " 2 6 3 894 13 1 2 3 5 5 2\n", " 3 2 2 28 807 0 10 1 8 6 8\n", " 4 17 0 20 0 913 11 35 11 13 38\n", " 5 14 2 4 19 3 751 26 1 14 2\n", " 6 7 3 11 10 6 18 870 4 5 4\n", " 7 2 0 17 11 9 4 1 934 4 28\n", " 8 12 6 26 134 8 80 12 5 916 27\n", " 9 5 0 13 8 32 5 1 41 4 889" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ - "X.p.test <- sweep(X.test/256, 2, m.X.p)\n", + "X.p.test <- sweep(X.test/255, 2, m.X.p)\n", "p3 <- predict(mn.features.fit, data.frame(relu(X.p.test %*% feature_vectors)))\n", "mean(data.test$Y == p3)\n", "table(p3, data.test$Y)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us turn now to learning the features with a neural network.\n", "We use `keras` here, as it is much faster than `ADtools`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "`geom_smooth()` using formula 'y ~ x'\n", "\n" ] }, { "data": { "image/png": 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GYhhBB2uz2TyXTAiJ0QYswQMaSPfcUG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\nT2wb51tft5sfOe1GRUA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QAAAID2I4Za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\n7/SELsJOGeIpyOKkrQcAAKD9CHdKsYFDBjBr5z/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JRxRFhULRZA1Rfe2YZbPZov0SZrPZbrfH2kfU5U2NjVEAACAASURBVKXe+c4cXFay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\nrOdsVt8mfCFCcblcROR0OiW8q+U4rvRzFLsQoZT+vnS5XBJuI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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "nn <- keras_model_sequential()\n", "nn %>%\n", " layer_dense(units = 200, activation = 'relu', input_shape = 784) %>%\n", " layer_dense(units = 10, activation = 'softmax') # with the softmax the outputs of the neurons indicate the probabilities of the digit classes (see slides)\n", "nn %>% compile(\n", " loss = 'categorical_crossentropy', # this is equivalent to choosing the negative log-likelihood loss (see slides)\n", " optimizer = 'adam', # this is a fancy version of stochastic gradient descent (usually you don't need to tune the learning rate with ADAM)\n", " metrics = c('accuracy') # we also track the accuracy during learning.\n", ")\n", "history <- nn %>% fit(\n", " X.p, to_categorical(data.train$Y), # the target is encoded as a categorical variable (this needs to be done explicitly for keras)\n", " epochs = 10, batch_size = 128,\n", " validation_split = 0\n", ")\n", "plot(history)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "In the plot you see how the training loss decreases (this is the negative\n", "log-likelihood loss which we optimize) and at the same time the classification\n", "accuracy on the training set increases.\n", "\n", "Next we compute test loss and accuracy:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "
loss
0.0706448331475258
accuracy
0.979300022125244
\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[loss] 0.0706448331475258\n", "\\item[accuracy] 0.979300022125244\n", "\\end{description*}\n" ], "text/markdown": [ "loss\n", ": 0.0706448331475258accuracy\n", ": 0.979300022125244\n", "\n" ], "text/plain": [ " loss accuracy \n", "0.07064483 0.97930002 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nn %>% evaluate(X.p.test, to_categorical(data.test$Y))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Compare this result again to the ones obtained with LDA, multinomial regression\n", "and multinomial regression with hand-crafted features to see how impressively\n", "well the learned features work on this data set.\n", "\n", "In the following cell we extract the learned feature weigths and plot some of\n", "them." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 784
  2. 200
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 784\n", "\\item 200\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 784\n", "2. 200\n", "\n", "\n" ], "text/plain": [ "[1] 784 200" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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emF/XJAUr8X6GbygJOeYkqVbMvQL3DSFa8wb0MXd5aPLynk3TOxqmjsF3q4+0aH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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "weights <- nn$layers[[1]]$get_weights()[[1]]\n", "dim(weights)\n", "par(mfrow = c(4, 6), oma = c(0, 0, 0, 0),\n", " mar = c(.1, .1, .1, .1), pty=\"s\")\n", "for (i in sample(1:200, 24)) {\n", " image(t(array_reshape(weights[,i], c(28, 28))[28:1,]), col = gray.colors(256, rev = T), axes = FALSE)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Review again the slide on nomenclature and loss versus accuracy in the lecture\n", "and once you are ready, please head over to the\n", "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1109835) and answer the\n", "questions on the first page.\n", "\n", "## Convolutional Neural Networks" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "We do not construct the random Gabor features here. If you are interested you\n", "can read more about [Gabor filters on\n", "Wikipedia](https://en.wikipedia.org/wiki/Gabor_filter). Here we move directly to\n", "convolutional neural networks.\n", "\n", "First we reshape the data again to be images of 28x28x1 pixels. The 1 at the end\n", "is used to indicate that we are dealing with gray-scale images; it would be 3,\n", "if we had colour images. Remember that in the video we used volumes to describe\n", "convolutional neural networks. Here the input is 28x28x1 dimensional volume." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "X.p.c <- array_reshape(X.p, c(nrow(X.p), 28, 28, 1))\n", "X.p.c.test <- array_reshape(X.p.test, c(nrow(X.p.test), 28, 28, 1))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we create our first convolutional neural network.\n", "We will use one convolutional layer with filters of size 10x10, padding 0 (keras\n", "option 'valid'), and stride 1. The output volume of this convolutional layer can\n", "be computed with the formula from the slides to get 19x19x200. Before we feed\n", "this volume to the classifier with 10 softmax neurons, we need to flatten this\n", "volume to a vector of length $19\\cdot19\\cdot200 = 72200$. This is done with the\n", "special layer `layer_flatten()` below." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "conv.nn <- keras_model_sequential()\n", "conv.nn %>%\n", " layer_conv_2d(200, # number of filters\n", " kernel_size = c(10, 10), # size of the filter\n", " strides = c(1, 1), # stride in x and y dimension\n", " activation = 'relu',\n", " input_shape = c(28, 28, 1)) %>%\n", " layer_flatten() %>% # (see text above)\n", " layer_dense(units = 10, activation = 'softmax')" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "With the `summary` function we can confirm the volume computation we did above:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: \"sequential_1\"\n", "________________________________________________________________________________\n", "Layer (type) Output Shape Param # \n", "================================================================================\n", "conv2d (Conv2D) (None, 19, 19, 200) 20200 \n", "________________________________________________________________________________\n", "flatten (Flatten) (None, 72200) 0 \n", "________________________________________________________________________________\n", "dense_2 (Dense) (None, 10) 722010 \n", "================================================================================\n", "Total params: 742,210\n", "Trainable params: 742,210\n", "Non-trainable params: 0\n", "________________________________________________________________________________\n" ] } ], "source": [ "summary(conv.nn)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us now compile and fit this convolutional network." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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h0AAIAkCHYAAACSINgBAADE5Msvvxw5cmRWVlbnzp1nzpzp9XqNqoRgBwAAcPq2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PxyY3pmobFWw/a9BvRqecXXUvjPpa9Z9c3+C8bYRm26\nD+hd9t0Snt2LXl91sctjY/vVL9/x5Nrp83bGDpjwcDITegD+IwQ7APj3lAe7zaMTtS4FAP41\n1tgBAAAogmAHAACgCG6eAIB/T2KvpyabI5OdWtcBAL+JNXYAAACK4FIsAACAIgh2AAAAiiDY\nAQAAKIJgBwAAoAiCHQAAgCIIdgAAAIog2AEAACji/wATnFbCBcBKdQAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "conv.nn %>% compile(\n", " loss = 'categorical_crossentropy',\n", " optimizer = 'adam',\n", " metrics = c('accuracy')\n", ")\n", "history <- conv.nn %>% fit(\n", " X.p.c, to_categorical(data.train$Y),\n", " epochs = 5, batch_size = 128,\n", " validation_split = 0\n", ")\n", "plot(history)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Let us compute the test loss and accuracy." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
loss
0.0442366041243076
accuracy
0.986500024795532
\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[loss] 0.0442366041243076\n", "\\item[accuracy] 0.986500024795532\n", "\\end{description*}\n" ], "text/markdown": [ "loss\n", ": 0.0442366041243076accuracy\n", ": 0.986500024795532\n", "\n" ], "text/plain": [ " loss accuracy \n", "0.0442366 0.9865000 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "conv.nn %>% evaluate(X.p.c.test, to_categorical(data.test$Y))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "And plot some of the learned filters." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 10
  2. 10
  3. 1
  4. 200
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 10\n", "\\item 10\n", "\\item 1\n", "\\item 200\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 10\n", "2. 10\n", "3. 1\n", "4. 200\n", "\n", "\n" ], "text/plain": [ "[1] 10 10 1 200" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "filters <- conv.nn$layers[[1]]$get_weights()[[1]]\n", "dim(filters)\n", "par(mfrow = c(4, 6), oma = c(0, 0, 0, 0),\n", " mar = c(.1, .1, .1, .1), pty=\"s\")\n", "for (i in sample(1:64, 24)) {\n", " image(t(array_reshape(filters[,,,i], c(10, 10))[10:1, 1:10]), col = gray.colors(256),\n", " axes = FALSE, xaxs = 'r', yaxs = 'i')\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once you are ready, please head over to the\n", "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1109835) and answer the\n", "questions on the second page.\n", "\n", "## Transfer Learning (optional)\n", "\n", "The following video is short and optional, but demonstrates a nice idea with\n", "cool applications: the learned features of a neural network trained on a really\n", "large dataset can be used as fixed features to obtain good performance on a\n", "smaller dataset." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "IRdisplay::display_html('')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is no code for this section.\n", "\n", "If you are interested you can look at the code for applying transfer learning to\n", "the flowers data set\n", "[here](https://cran.r-project.org/web/packages/tfhub/vignettes/hub-with-keras.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularization and Early Stopping" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "lines_to_next_cell": 0 }, "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 a simple dataset. We will use the first 25 points as training data\n", "and the rest as validation set." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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NbAl8e1rN7nj/c7DWuyY2R5D9MJAQAAnIELFLsTe/eGK9NLfeJanSR5Fnllxjfr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C\n", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "set.seed(3)\n", "X <- 4*runif(50) - 2\n", "Y <- X^2 + rnorm(50)\n", "plot(X, Y, col = c(rep('red', 25), rep('blue', 25)))" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Because we will fit different neural networks below, I wrote the following\n", "helper function to compile and fit the neural network and make predictions on a\n", "grid. We include also the argument `callbacks` which will be useful for early\n", "stopping. We use the `mse` loss (Mean Squared Error), which is just the residual\n", "sum of squares (RSS) divided by the number of training samples. This is the\n", "standard negative log-likelihood loss for a regression problem." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "myfit <- function(nn, X, Y, grid = seq(-2, 2, length = 100), callbacks = NULL) {\n", " nn %>% compile(\n", " loss = 'mse',\n", " optimizer = 'adam'\n", " )\n", " history <- nn %>% fit(\n", " X, Y,\n", " validation_split = 0.5,\n", " callbacks = callbacks,\n", " epochs = 1500,\n", " )\n", " list(nn = nn, history = history, grid = grid, pred = predict(nn, grid))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Our first neural network has 2 hidden layers with 50 neurons each." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "`geom_smooth()` using formula 'y ~ x'\n", "\n" ] }, { "data": { "image/png": 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p6erqenFxsb27hxY9FZvsapWPoGDQ0NmUwWHBzM3wGIiNTL69evp0yZYmFhsXPn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+CwsLNze3j+xUvGkTqlZ9U9X9a/RoFC2K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\nAACKINgBAAAogmAHAACgCIIdAACAIgh2AAAAiiDYAQAAKIJgB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afTaTQapbMAAABkFSt26aLVAQCA/IViBwAAYCI4FJuuPXv2HDx4MDExsWbNmm3a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\nSVMsW4mu3fOmvmZm4qsv8fFYqNRwcoJKBSvXrk2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yxerL1/ZGxyrVao1GU9JCTO1eEKS2rtKvO7f3doQZkUsAACAASURBVFRD4G0LbtoH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\nwkL2Xs9LSkqiOqFji0udKHh5i7dVly4os660+LDbbrtt+/bt9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28wGILd3L7Kuj44wN9Lo1ErFBZBYBimi1c8kfDhUdzwFPE2xbLa3dsb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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "nn1 <- keras_model_sequential() %>%\n", " layer_dense(units = 50, activation = 'relu', input_shape = c(1)) %>%\n", " layer_dense(units = 50, activation = 'relu') %>%\n", " layer_dense(units = 1, activation = 'linear')\n", "res1 <- myfit(nn1, X, Y)\n", "plot(X, Y, col = c(rep('red', 25), rep('blue', 25)))\n", "lines(res1$grid, res1$pred)\n", "plot(res1$history)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Now we repeat the same with regularization in all layers." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "`geom_smooth()` using formula 'y ~ x'\n", "\n" ] }, { "data": { "image/png": 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67YaazChQvPmTPHy8urW7duFStWFB1HmMuXUaeOnNfLammhfn0kJorIRESkyk6f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\n9YGB+N//MHQo3NxQs6ao+YioHPCIHRGReoiMxP3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587d07pUAAAwKtR7MoiKSlp2rRp3wzs2y2iRuHIypOnH3nhhT59+gQEBCibDQAA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\ns2bo0KHl5eV1dXUejwcA/v73v9fX159//vlbtmxZunRpa2trbm6u1+utra0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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "nn2 <- keras_model_sequential() %>%\n", " layer_dense(units = 50, activation = 'relu', kernel_regularizer = regularizer_l2(l = .1), input_shape = c(1)) %>%\n", " layer_dense(units = 50, kernel_regularizer = regularizer_l2(l = .1), activation = 'relu') %>%\n", " layer_dense(units = 1, kernel_regularizer = regularizer_l2(l = .02), activation = 'linear')\n", "res2 <- myfit(nn2, X, Y)\n", "plot(X, Y, col = c(rep('red', 25), rep('blue', 25)))\n", "lines(res2$grid, res2$pred)\n", "plot(res2$history)" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 0 }, "source": [ "Finally, we do not use regularization, but use the callback\n", "`callback_early_stopping` that stops gradient descent when the validation loss\n", "`val_loss` starts to increase." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "`geom_smooth()` using formula 'y ~ x'\n", "\n" ] }, { "data": { "image/png": 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mQwOtHzo9ilCy1atDh69GjHjh2bN2/u7+//008//eWhSUlauFBt28rTU6+9pnfe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\nBwAAYBIUOwAAAJOg2AEAAJgExQ4AAMAkKHYAAAA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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" }, { "data": { "image/png": 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2NOUfFt0Uy2AwDg93wm2Alz6i2vT++zccueowXOkCE3pPbo0iTkdJfX4WzMZnNJ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\nj9yjMGHChMLCwva//WbN55UplN4NG65du9bBwUHXGx0dPfOrLxs52L3awFn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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "nn3 <- keras_model_sequential() %>%\n", " layer_dense(units = 50, activation = 'relu', input_shape = c(1)) %>%\n", " layer_dense(units = 50, activation = 'relu') %>%\n", " layer_dense(units = 1, activation = 'linear')\n", "callback <- callback_early_stopping(monitor = \"val_loss\")\n", "res3 <- myfit(nn3, X, Y, callbacks = callback)\n", "plot(X, Y, col = c(rep('red', 25), rep('blue', 25)))\n", "lines(res3$grid, res3$pred)\n", "res3$history$params$epochs <- length(res3$history$metrics$loss) # this is a hack to fix a problem of keras\n", "plot(res3$history)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once you are ready, please head over to the\n", "[quiz](https://moodle.epfl.ch/mod/quiz/view.php?id=1109835) and answer the\n", "questions on the third page.\n", "\n", "## Exercises\n", "\n", "### Conceptual\n", "\n", "**Q1**\n", "Here below there is an image we would like to process with a convolutional network with one convolution layer with two 3 $\\times$ 3 filters (depicted below the image) and relu non-linearity.\n", "\n", "![](img/Conv.PNG)\n", "\n", "(a) Determine the width, height and depth of the volume after the convolutional layer.\n", "\n", "(b) Compute the output of the convolutional layer assuming the two biases to be zero.\n", "\n", "**Q2**\n", "Given a volume of width $n$, height $n$ and depth $c$:\n", "\n", "(a) Convince yourself that the convolution with $k$ filters of size $f\\times f\\times c$ with stride $s$ and padding $p$ leads to a new volume of size\n", "\\begin{equation*}\n", " \\left( \\frac{n + 2p - f}{s} + 1\\right)\\times \\left( \\frac{n + 2p - f}{s} + 1\\right)\\times k\\, .\n", "\\end{equation*}\n", "\n", "(b) Keras knows the padding options `valid` and `same`. The first one, `valid`,\n", "means no padding at all. The second one, `same`, means that the output volume\n", "should have the same x and y dimension as the input volume. In this exercise we\n", "compute the padding needed for option `same`.\n", "What padding $p$ do you have to choose such that the input and output volumes have the same width and depth for stride $s=1$. Check you result for the special case of $n=4$ and $f=3$.\n", "\n", "## Applied\n", "\n", "**Q3**\n", "In this exercise you will try to identify metastatic tissue in histopathologic scans of lymph node sections. The input data consists of greyscale images of 32 $\\times$ 32 pixels that were derived from the Histopathalogic Cancer Detection competition (https://www.kaggle.com/c/histopathologic-cancer-detection).\n", "The original dataset contains colour image patches of 96 $\\times$ 96 pixels taken from larger digital pathology scans ($220\\,025$ in the training set, and $57\\,458$ in the test set).\n", "A positive label indicates that the central 32 $\\times$ 32 pixels region contains at least one pixel of tumor tissue.\n", "For this exercise we look at $40\\,000$ images from the training set, where the central patch of the original image was extracted and transformed to greyscale to reduce the computational burden.\n", "\n", "(a) Load the data with the command\n", "`load(url(\"https://lcnwww.epfl.ch/bio322/PCaml.rda\"))`; two new variables will be added to your workspace: `PCaml_x` and `PCaml_y`.\n", "\n", "(b) In general it is recommendable to look at the raw data first. Here, you may want to plot 24 randomly chosen example images that were labelled to contain at least one pixel of tumor tissue and 24 randomly chosen images that were labelled as tumor-free samples. Can you see by eye any difference between the two classes?\n", "\n", "(c) Split the data into a training set of size $n=30\\,000$ and a test set of size $n=10\\,000$.\n", "\n", "(d) Perform logistic regression to have a benchmark.\n", "Plot the ROC, compute the AUC and compute the accuracy on the training and test set.\n", "\n", "(e) Fit a convolutional neural network to the data.\n", "Compare ROC, AUC and accuracy of the neural network fit to the logistic regression fit.\n", "\n", "(f) (Optional) Play with the network architecture. You may change the number of filters per convolutional layer, the number of layers, add regularization etc. and see how the test error depends on your architectural choices." ] } ], "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 }