|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "6cc2501d", |
| 6 | + "metadata": { |
| 7 | + "editable": true |
| 8 | + }, |
| 9 | + "source": [ |
| 10 | + "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n", |
| 11 | + "doconce format html exercisesweek47.do.txt -->\n", |
| 12 | + "<!-- dom:TITLE: Exercise week 47-48 -->" |
| 13 | + ] |
| 14 | + }, |
| 15 | + { |
| 16 | + "cell_type": "markdown", |
| 17 | + "id": "7aae5111", |
| 18 | + "metadata": { |
| 19 | + "editable": true |
| 20 | + }, |
| 21 | + "source": [ |
| 22 | + "# Exercise week 47-48\n", |
| 23 | + "**November 17-28, 2025**\n", |
| 24 | + "\n", |
| 25 | + "Date: **Deadline is Friday November 28 at midnight**" |
| 26 | + ] |
| 27 | + }, |
| 28 | + { |
| 29 | + "cell_type": "markdown", |
| 30 | + "id": "5ef837a4", |
| 31 | + "metadata": { |
| 32 | + "editable": true |
| 33 | + }, |
| 34 | + "source": [ |
| 35 | + "# Overarching aims of the exercises this week\n", |
| 36 | + "\n", |
| 37 | + "The exercise set this week is meant as a summary of many of the\n", |
| 38 | + "central elements in various machine learning algorithms we have discussed throught the semester. You don't need to answer all questions." |
| 39 | + ] |
| 40 | + }, |
| 41 | + { |
| 42 | + "cell_type": "markdown", |
| 43 | + "id": "3f1ef66b", |
| 44 | + "metadata": { |
| 45 | + "editable": true |
| 46 | + }, |
| 47 | + "source": [ |
| 48 | + "## Linear and logistic regression methods" |
| 49 | + ] |
| 50 | + }, |
| 51 | + { |
| 52 | + "cell_type": "markdown", |
| 53 | + "id": "e86c9231", |
| 54 | + "metadata": { |
| 55 | + "editable": true |
| 56 | + }, |
| 57 | + "source": [ |
| 58 | + "### Question 1:\n", |
| 59 | + "\n", |
| 60 | + "Which of the following is not an assumption of ordinary least squares linear regression?\n", |
| 61 | + "\n", |
| 62 | + "* There is a linearity between predictors/features and target/outout\n", |
| 63 | + "\n", |
| 64 | + " * The inputs/features distributed according to a normal/gaussian distribution" |
| 65 | + ] |
| 66 | + }, |
| 67 | + { |
| 68 | + "cell_type": "markdown", |
| 69 | + "id": "9acef906", |
| 70 | + "metadata": { |
| 71 | + "editable": true |
| 72 | + }, |
| 73 | + "source": [ |
| 74 | + "### Question 2:\n", |
| 75 | + "\n", |
| 76 | + "The mean squared error cost function for linear regression is convex in the parameters, guaranteeing a unique global minimum. True or False? Motivate your answer." |
| 77 | + ] |
| 78 | + }, |
| 79 | + { |
| 80 | + "cell_type": "markdown", |
| 81 | + "id": "fb3bf02e", |
| 82 | + "metadata": { |
| 83 | + "editable": true |
| 84 | + }, |
| 85 | + "source": [ |
| 86 | + "### Question 3:\n", |
| 87 | + "\n", |
| 88 | + "Which statement about logistic regression is false?\n", |
| 89 | + "\n", |
| 90 | + "* Logistic regression is used for binary classification.\n", |
| 91 | + "\n", |
| 92 | + " * It uses the sigmoid function to map linear scores to probabilities.\n", |
| 93 | + "\n", |
| 94 | + " * It has an analytical closed-form solution.\n", |
| 95 | + "\n", |
| 96 | + " * Its log-loss (cross-entropy) is convex." |
| 97 | + ] |
| 98 | + }, |
| 99 | + { |
| 100 | + "cell_type": "markdown", |
| 101 | + "id": "e8ab306a", |
| 102 | + "metadata": { |
| 103 | + "editable": true |
| 104 | + }, |
| 105 | + "source": [ |
| 106 | + "### Question 4:\n", |
| 107 | + "\n", |
| 108 | + "Logistic regression produces a linear decision boundary in the input space. True or False? Explain." |
| 109 | + ] |
| 110 | + }, |
| 111 | + { |
| 112 | + "cell_type": "markdown", |
| 113 | + "id": "d695e6bb", |
| 114 | + "metadata": { |
| 115 | + "editable": true |
| 116 | + }, |
| 117 | + "source": [ |
| 118 | + "### Question 5:\n", |
| 119 | + "\n", |
| 120 | + "Give two reasons why logistic regression is preferred over linear regression for binary classification." |
| 121 | + ] |
| 122 | + }, |
| 123 | + { |
| 124 | + "cell_type": "markdown", |
| 125 | + "id": "8c398642", |
| 126 | + "metadata": { |
| 127 | + "editable": true |
| 128 | + }, |
| 129 | + "source": [ |
| 130 | + "## Neural networks" |
| 131 | + ] |
| 132 | + }, |
| 133 | + { |
| 134 | + "cell_type": "markdown", |
| 135 | + "id": "f58fac35", |
| 136 | + "metadata": { |
| 137 | + "editable": true |
| 138 | + }, |
| 139 | + "source": [ |
| 140 | + "### Question 6:\n", |
| 141 | + "\n", |
| 142 | + "Which statement is not true for fully-connected neural networks?\n", |
| 143 | + "\n", |
| 144 | + "* Without nonlinear activation functions they reduce to a single linear model.\n", |
| 145 | + "\n", |
| 146 | + " * Training relies on backpropagation using the chain rule.\n", |
| 147 | + "\n", |
| 148 | + " * A single hidden layer can approximate any continuous function on a compact set.\n", |
| 149 | + "\n", |
| 150 | + " * The loss surface of a deep neural network is convex." |
| 151 | + ] |
| 152 | + }, |
| 153 | + { |
| 154 | + "cell_type": "markdown", |
| 155 | + "id": "9bed2727", |
| 156 | + "metadata": { |
| 157 | + "editable": true |
| 158 | + }, |
| 159 | + "source": [ |
| 160 | + "### Question 7:\n", |
| 161 | + "\n", |
| 162 | + "Using sigmoid activations in many layers of a deep neural network can cause vanishing gradients. True or False? Explain." |
| 163 | + ] |
| 164 | + }, |
| 165 | + { |
| 166 | + "cell_type": "markdown", |
| 167 | + "id": "e3c1865d", |
| 168 | + "metadata": { |
| 169 | + "editable": true |
| 170 | + }, |
| 171 | + "source": [ |
| 172 | + "### Question 8:\n", |
| 173 | + "\n", |
| 174 | + "Describe the vanishing gradient problem: Why does it occur? Mention one technique to mitigate it and explain briefly." |
| 175 | + ] |
| 176 | + }, |
| 177 | + { |
| 178 | + "cell_type": "markdown", |
| 179 | + "id": "6d1ad1a8", |
| 180 | + "metadata": { |
| 181 | + "editable": true |
| 182 | + }, |
| 183 | + "source": [ |
| 184 | + "### Question 9:\n", |
| 185 | + "\n", |
| 186 | + "Consider a fully-connected network with layer sizes $n_0$ (the input\n", |
| 187 | + "layer) ,$n_1$ (first hidden layer), $\\dots, n_L$, where $n_L$ is the\n", |
| 188 | + "output layer. Derive a general formula for the total number of\n", |
| 189 | + "trainable parameters (weights + biases)." |
| 190 | + ] |
| 191 | + }, |
| 192 | + { |
| 193 | + "cell_type": "markdown", |
| 194 | + "id": "f5b2ed47", |
| 195 | + "metadata": { |
| 196 | + "editable": true |
| 197 | + }, |
| 198 | + "source": [ |
| 199 | + "## Convolutional Neural Networks" |
| 200 | + ] |
| 201 | + }, |
| 202 | + { |
| 203 | + "cell_type": "markdown", |
| 204 | + "id": "93d54a83", |
| 205 | + "metadata": { |
| 206 | + "editable": true |
| 207 | + }, |
| 208 | + "source": [ |
| 209 | + "### Question 10:\n", |
| 210 | + "\n", |
| 211 | + "Which of the following is not a typical property or advantage of CNNs?\n", |
| 212 | + "\n", |
| 213 | + "* Local receptive fields\n", |
| 214 | + "\n", |
| 215 | + " * Weight sharing\n", |
| 216 | + "\n", |
| 217 | + " * More parameters than fully-connected layers\n", |
| 218 | + "\n", |
| 219 | + " * Pooling layers offering some translation invariance" |
| 220 | + ] |
| 221 | + }, |
| 222 | + { |
| 223 | + "cell_type": "markdown", |
| 224 | + "id": "5aefcc46", |
| 225 | + "metadata": { |
| 226 | + "editable": true |
| 227 | + }, |
| 228 | + "source": [ |
| 229 | + "### Question 11:\n", |
| 230 | + "\n", |
| 231 | + "Using zero-padding in convolutional layers can preserve the input\n", |
| 232 | + "spatial dimensions when using a $3 \\times 3$ kernel/filter, stride 1,\n", |
| 233 | + "and padding $P = 1$. True or False?" |
| 234 | + ] |
| 235 | + }, |
| 236 | + { |
| 237 | + "cell_type": "markdown", |
| 238 | + "id": "348b6806", |
| 239 | + "metadata": { |
| 240 | + "editable": true |
| 241 | + }, |
| 242 | + "source": [ |
| 243 | + "### Question 12:\n", |
| 244 | + "\n", |
| 245 | + "Given input width $W$, kernel size $K$, stride S, and padding P,\n", |
| 246 | + "derive the formula for the output width $W_{\\text{out}} = \\frac{W - K+ 2P}{S} + 1$." |
| 247 | + ] |
| 248 | + }, |
| 249 | + { |
| 250 | + "cell_type": "markdown", |
| 251 | + "id": "a629397f", |
| 252 | + "metadata": { |
| 253 | + "editable": true |
| 254 | + }, |
| 255 | + "source": [ |
| 256 | + "### Question 13:\n", |
| 257 | + "\n", |
| 258 | + "A convolutional layer has: $C_{\\text{in}}$ input channels,\n", |
| 259 | + "$C_{\\text{out}}$ output channels (filters) and kernel size $K_h \\times\n", |
| 260 | + "K_w$. Compute the number of trainable parameters including biases." |
| 261 | + ] |
| 262 | + }, |
| 263 | + { |
| 264 | + "cell_type": "markdown", |
| 265 | + "id": "087780b2", |
| 266 | + "metadata": { |
| 267 | + "editable": true |
| 268 | + }, |
| 269 | + "source": [ |
| 270 | + "## Recurrent Neural Networks" |
| 271 | + ] |
| 272 | + }, |
| 273 | + { |
| 274 | + "cell_type": "markdown", |
| 275 | + "id": "55dd5f95", |
| 276 | + "metadata": { |
| 277 | + "editable": true |
| 278 | + }, |
| 279 | + "source": [ |
| 280 | + "### Question 14:\n", |
| 281 | + "\n", |
| 282 | + "Which statement about simple RNNs is false?\n", |
| 283 | + "\n", |
| 284 | + "* They maintain a hidden state updated each time step.\n", |
| 285 | + "\n", |
| 286 | + " * They use the same weight matrices at every time step.\n", |
| 287 | + "\n", |
| 288 | + " * They handle sequences of arbitrary length.\n", |
| 289 | + "\n", |
| 290 | + " * They eliminate the vanishing gradient problem." |
| 291 | + ] |
| 292 | + }, |
| 293 | + { |
| 294 | + "cell_type": "markdown", |
| 295 | + "id": "fd70bb6d", |
| 296 | + "metadata": { |
| 297 | + "editable": true |
| 298 | + }, |
| 299 | + "source": [ |
| 300 | + "### Question 15:\n", |
| 301 | + "\n", |
| 302 | + "LSTMs mitigate the vanishing gradient problem by using gating mechanisms (input, forget, output gates). True or False? Explain." |
| 303 | + ] |
| 304 | + }, |
| 305 | + { |
| 306 | + "cell_type": "markdown", |
| 307 | + "id": "ab7ec77a", |
| 308 | + "metadata": { |
| 309 | + "editable": true |
| 310 | + }, |
| 311 | + "source": [ |
| 312 | + "### Question 16:\n", |
| 313 | + "\n", |
| 314 | + "What is Backpropagation Through Time (BPTT) and why is it required for training RNNs?" |
| 315 | + ] |
| 316 | + }, |
| 317 | + { |
| 318 | + "cell_type": "markdown", |
| 319 | + "id": "e32e01d4", |
| 320 | + "metadata": { |
| 321 | + "editable": true |
| 322 | + }, |
| 323 | + "source": [ |
| 324 | + "### Question 17:\n", |
| 325 | + "\n", |
| 326 | + "What does a sliding window do? And why would we use it?" |
| 327 | + ] |
| 328 | + } |
| 329 | + ], |
| 330 | + "metadata": {}, |
| 331 | + "nbformat": 4, |
| 332 | + "nbformat_minor": 5 |
| 333 | +} |
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