├── README.md ├── data ├── kirby127a_3_1_ax_283Labels_M2_corrected_stats.csv ├── kirby21.csv ├── oasis.csv ├── orings.csv └── swiss.csv ├── notebooks ├── EDA.ipynb ├── Intro_to_DFT.ipynb ├── Least_squares_correction.ipynb ├── LinearModels_and_FFTs.ipynb ├── basicRegression _in_pytorch.ipynb ├── logisticRegression_in_pytorch.ipynb ├── multivariable_nn_in_torch.ipynb ├── notebook1.ipynb ├── notebook2.ipynb ├── notebook3.ipynb ├── notebook4.ipynb ├── notebook5.ipynb ├── notebook5_a.ipynb ├── notebook6.ipynb ├── regression_examples.ipynb ├── regression_through_the_origin.ipynb └── tensorflow_example.ipynb ├── old ├── labSyllabus.md ├── syllabus.md └── test └── presentations ├── lecture1.html ├── lecture1.org ├── lecture2.html └── lecture2.org /README.md: -------------------------------------------------------------------------------- 1 | # ds4bme_intro 2 | 3 | A **github** repo for the intro to data science for BME (ds4bme_intro) course where we will post code, open access data and jupyter notebooks. 4 | 5 | Please go to the Teams site for course information 6 | 7 | 8 | 9 | -------------------------------------------------------------------------------- /data/oasis.csv: -------------------------------------------------------------------------------- 1 | "FLAIR","PD","T1","T2","FLAIR_10","PD_10","T1_10","T2_10","FLAIR_20","PD_20","T1_20","T2_20","GOLD_Lesions" 2 | 1.14369177818298,1.58621907234192,-0.799859464168549,1.63446724414825,0.437568068504333,0.823800206184387,-0.00205940613523126,0.573662877082825,0.279831767082214,0.548341274261475,0.219135880470276,0.298661708831787,0 3 | 1.65255188941956,1.76667249202728,-1.25099194049835,0.921229839324951,0.663036644458771,0.880249798297882,-0.422059565782547,0.542597413063049,0.422182232141495,0.549710631370544,0.0615727305412292,0.280972093343735,0 4 | 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| "18",75,0,2,1 20 | "19",76,0,0,0 21 | "20",76,0,0,0 22 | "21",78,0,0,0 23 | "22",79,0,0,0 24 | "23",81,0,0,0 25 | -------------------------------------------------------------------------------- /data/swiss.csv: -------------------------------------------------------------------------------- 1 | "Region","Fertility","Agriculture","Examination","Education","Catholic","Infant.Mortality" 2 | "Courtelary",80.2,17,15,12,9.96,22.2 3 | "Delemont",83.1,45.1,6,9,84.84,22.2 4 | "Franches-Mnt",92.5,39.7,5,5,93.4,20.2 5 | "Moutier",85.8,36.5,12,7,33.77,20.3 6 | "Neuveville",76.9,43.5,17,15,5.16,20.6 7 | "Porrentruy",76.1,35.3,9,7,90.57,26.6 8 | "Broye",83.8,70.2,16,7,92.85,23.6 9 | "Glane",92.4,67.8,14,8,97.16,24.9 10 | "Gruyere",82.4,53.3,12,7,97.67,21 11 | "Sarine",82.9,45.2,16,13,91.38,24.4 12 | "Veveyse",87.1,64.5,14,6,98.61,24.5 13 | "Aigle",64.1,62,21,12,8.52,16.5 14 | "Aubonne",66.9,67.5,14,7,2.27,19.1 15 | "Avenches",68.9,60.7,19,12,4.43,22.7 16 | "Cossonay",61.7,69.3,22,5,2.82,18.7 17 | 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Locle",72.7,16.7,22,13,11.22,18.9 43 | "Neuchatel",64.4,17.6,35,32,16.92,23 44 | "Val de Ruz",77.6,37.6,15,7,4.97,20 45 | "ValdeTravers",67.6,18.7,25,7,8.65,19.5 46 | "V. De Geneve",35,1.2,37,53,42.34,18 47 | "Rive Droite",44.7,46.6,16,29,50.43,18.2 48 | "Rive Gauche",42.8,27.7,22,29,58.33,19.3 49 | -------------------------------------------------------------------------------- /notebooks/Least_squares_correction.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "Least squares correction", 7 | "provenance": [], 8 | "authorship_tag": "ABX9TyMy2ynmrp6kOLuGKXg266mN", 9 | "include_colab_link": true 10 | }, 11 | "kernelspec": { 12 | "name": "python3", 13 | "display_name": "Python 3" 14 | } 15 | }, 16 | "cells": [ 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "id": "view-in-github", 21 | "colab_type": "text" 22 | }, 23 | "source": [ 24 | "\"Open" 25 | ] 26 | }, 27 | { 28 | "cell_type": "markdown", 29 | "metadata": { 30 | "id": "558cC4d_R8kq", 31 | "colab_type": "text" 32 | }, 33 | "source": [ 34 | "# Least sqaures proof of minimization for regression through the origin\n", 35 | "\n", 36 | "Consider minimizing $\\sum_{i=1}^n (y_i - \\beta x_i)^2 = f(\\beta)$.\n", 37 | "\n", 38 | "The first derivative is\n", 39 | "$$\n", 40 | "f'(\\beta) = -2\\sum_{i=1}^n y_i x_i + 2\\beta \\sum_{i=1}^n x_i^2.\n", 41 | "$$\n", 42 | "\n", 43 | "Setting equal to 0, this yeilds the solution\n", 44 | "$$\n", 45 | "\\hat \\beta = \\frac{\\sum_{i=1}^n y_i x_i}{\\sum_{i=1}^n x_i^2}.\n", 46 | "$$\n", 47 | "\n", 48 | "The second derivative is\n", 49 | "$$\n", 50 | "f''(\\beta) = 2\\sum_{i=1}^n x_i^2 \n", 51 | "$$\n", 52 | "which is strictly positive provided any $x_i \\neq 0$. Thus, excepting the case where all $x_i$ are 0, $f$ is convex and so the root of our derivative is indeed a minimum." 53 | ] 54 | }, 55 | { 56 | "cell_type": "markdown", 57 | "metadata": { 58 | "id": "du5kEWjkTukl", 59 | "colab_type": "text" 60 | }, 61 | "source": [ 62 | "# (optional) More generic proof that doesn't require differentiation and works for $x$ and $y$ as functions or any other algebraic object\n", 63 | "\n", 64 | "Let $x$ an $y$ be objects that exist in a space with an inner product $<,>$ and norm, $||a||^2 = $ that follow the standard rules (often such a space is called a Hilbert space). We show that $\\hat \\beta = /$ is the unique minimizer of $||y - \\beta x||^2$ . (Note this proof requires that you know the answer and isn't constructive, like the derivative proof when $x$ and $y$ are real vector).\n", 65 | "\n", 66 | "$$\n", 67 | "\\begin{align} \n", 68 | "||y - \\beta x||^2 & = ||y - \\hat \\beta x + \\hat\\beta x - \\beta x||^2 \\\\\n", 69 | "& = ||y - \\hat \\beta x||^2 + 2 \n", 70 | "+ ||\\hat\\beta x - \\beta x||^2 \\\\\n", 71 | "& = ||y - \\hat \\beta x||^2 + 2 \\hat \\beta - 2 \\beta + 2 \\hat \\beta^2 + 2 \\hat\\beta\\beta + ||\\hat\\beta x - \\beta x||^2 \\\\\n", 72 | "& = ||y - \\hat \\beta x||^2 +\n", 73 | "2\\frac{^2}{||x||^2} - 2 \\beta + 2\\frac{^2}{||x||^2} + 2 \\beta + ||\\hat\\beta x - \\beta x||^2 \\\\\n", 74 | "& = ||y - \\hat \\beta x||^2 + ||\\hat\\beta x - \\beta x||^2 \\\\\n", 75 | "& \\geq ||y - \\hat \\beta x||^2\n", 76 | "\\end{align}\n", 77 | "$$\n", 78 | "The inequality comes about since $||\\hat\\beta x - \\beta x||^2$ is necessarily non-negative so that dropping it can only make the quanitity smaller. Thus, \n", 79 | "for any $\\beta$, the quantity $||y - \\hat \\beta x||^2$ is larger than $||y - \\hat \\beta x||^2$ and so $\\hat \\beta$ must be the minimum.\n", 80 | "\n", 81 | "Note, I used some rules about inner products there.\n", 82 | "\n", 83 | "* $ = + + + $\n", 84 | "* $ = = c$ for constant $c$\n", 85 | "\n", 86 | "Example, let $ = \\int_0^1 f(t) g(t) dt$ for functions on $[0,1]$. Let $x = 1$ (i.e. the constant function) and let $y$ be any function. What's the best approximation of $y$ of the form $\\beta x$? According to our result, it has to be \n", 87 | "$$\n", 88 | "\\frac{}{||x||^2} = = \\int_0^1 y(t) dt.\n", 89 | "$$\n", 90 | "So, if you define $\\bar y = \\int_0^1 y(t) dt$ as the average, it's still the best approximation if you have no information." 91 | ] 92 | } 93 | ] 94 | } -------------------------------------------------------------------------------- /notebooks/logisticRegression_in_pytorch.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "logisticRegression in pytorch", 7 | "provenance": [], 8 | "collapsed_sections": [], 9 | "machine_shape": "hm", 10 | "include_colab_link": true 11 | }, 12 | "kernelspec": { 13 | "name": "python3", 14 | "display_name": "Python 3" 15 | } 16 | }, 17 | "cells": [ 18 | { 19 | "cell_type": "markdown", 20 | "metadata": { 21 | "id": "view-in-github", 22 | "colab_type": "text" 23 | }, 24 | "source": [ 25 | "\"Open" 26 | ] 27 | }, 28 | { 29 | "cell_type": "markdown", 30 | "metadata": { 31 | "id": "uiVM4lOtpJVt" 32 | }, 33 | "source": [ 34 | "This is an extension of using pytorch to perform linear regression to using it to perform logistic regression." 35 | ] 36 | }, 37 | { 38 | "cell_type": "code", 39 | "metadata": { 40 | "id": "6nKZWgTDvTTK", 41 | "outputId": "264fb349-cfa2-42cd-ddb4-1efc49f2d883", 42 | "colab": { 43 | "base_uri": "https://localhost:8080/", 44 | "height": 195 45 | } 46 | }, 47 | "source": [ 48 | "import pandas as pd\n", 49 | "import torch\n", 50 | "import statsmodels.formula.api as smf\n", 51 | "import statsmodels as sm\n", 52 | "import seaborn as sns\n", 53 | "import matplotlib.pyplot as plt\n", 54 | "import numpy as np\n", 55 | "\n", 56 | "## Read in the data and display a few rows\n", 57 | "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")\n", 58 | "dat.head(4)\n", 59 | "\n", 60 | "## Create a binary outcome variable (people will use gold lesions in HW)\n", 61 | "m = np.median(dat.T2)\n", 62 | "dat = dat.assign(y = (dat.T2 > m) * 1 )\n", 63 | "## Create a normalized regression variable\n", 64 | "dat = dat.assign(x = (dat.PD - np.mean(dat.PD)) / np.std(dat.PD))\n", 65 | "dat.head()\n" 66 | ], 67 | "execution_count": 113, 68 | "outputs": [ 69 | { 70 | "output_type": "execute_result", 71 | "data": { 72 | "text/html": [ 73 | "
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FLAIRPDT1T2FLAIR_10PD_10T1_10T2_10FLAIR_20PD_20T1_20T2_20GOLD_Lesionsyx
01.1436921.586219-0.7998591.6344670.4375680.823800-0.0020590.5736630.2798320.5483410.2191360.298662011.181648
11.6525521.766672-1.2509920.9212300.6630370.880250-0.4220600.5425970.4221820.5497110.0615730.280972011.426453
21.0360990.262042-0.858565-0.058211-0.044280-0.3085690.014766-0.256075-0.136532-0.3509050.020673-0.25991400-0.614749
31.0376920.011104-1.228796-0.470222-0.013971-0.000498-0.395575-0.2219000.000807-0.003085-0.193249-0.13928400-0.955175
41.5805891.730152-0.8609491.2456090.6179570.866352-0.0999190.3842610.3911330.6088260.0716480.340601011.376909
\n", 201 | "
" 202 | ], 203 | "text/plain": [ 204 | " FLAIR PD T1 T2 ... T2_20 GOLD_Lesions y x\n", 205 | "0 1.143692 1.586219 -0.799859 1.634467 ... 0.298662 0 1 1.181648\n", 206 | "1 1.652552 1.766672 -1.250992 0.921230 ... 0.280972 0 1 1.426453\n", 207 | "2 1.036099 0.262042 -0.858565 -0.058211 ... -0.259914 0 0 -0.614749\n", 208 | "3 1.037692 0.011104 -1.228796 -0.470222 ... -0.139284 0 0 -0.955175\n", 209 | "4 1.580589 1.730152 -0.860949 1.245609 ... 0.340601 0 1 1.376909\n", 210 | "\n", 211 | "[5 rows x 15 columns]" 212 | ] 213 | }, 214 | "metadata": { 215 | "tags": [] 216 | }, 217 | "execution_count": 113 218 | } 219 | ] 220 | }, 221 | { 222 | "cell_type": "code", 223 | "metadata": { 224 | "id": "ehiVfmYHJ4EL", 225 | "outputId": "eb701a2c-88e2-46ee-b2cf-3d5b6cc8eaa8", 226 | "colab": { 227 | "base_uri": "https://localhost:8080/", 228 | "height": 290 229 | } 230 | }, 231 | "source": [ 232 | "fit = smf.logit('y ~ x', data = dat).fit()\n", 233 | "fit.summary()" 234 | ], 235 | "execution_count": 114, 236 | "outputs": [ 237 | { 238 | "output_type": "stream", 239 | "text": [ 240 | "Optimization terminated successfully.\n", 241 | " Current function value: 0.427855\n", 242 | " Iterations 7\n" 243 | ], 244 | "name": "stdout" 245 | }, 246 | { 247 | "output_type": "execute_result", 248 | "data": { 249 | "text/html": [ 250 | "\n", 251 | "\n", 252 | "\n", 253 | " \n", 254 | "\n", 255 | "\n", 256 | " \n", 257 | "\n", 258 | "\n", 259 | " \n", 260 | "\n", 261 | "\n", 262 | " \n", 263 | "\n", 264 | "\n", 265 | " \n", 266 | "\n", 267 | "\n", 268 | " \n", 269 | "\n", 270 | "\n", 271 | " \n", 272 | "\n", 273 | "
Logit Regression Results
Dep. Variable: y No. Observations: 100
Model: Logit Df Residuals: 98
Method: MLE Df Model: 1
Date: Wed, 30 Sep 2020 Pseudo R-squ.: 0.3827
Time: 02:50:12 Log-Likelihood: -42.785
converged: True LL-Null: -69.315
Covariance Type: nonrobust LLR p-value: 3.238e-13
\n", 274 | "\n", 275 | "\n", 276 | " \n", 277 | "\n", 278 | "\n", 279 | " \n", 280 | "\n", 281 | "\n", 282 | " \n", 283 | "\n", 284 | "
coef std err z P>|z| [0.025 0.975]
Intercept 0.0367 0.269 0.136 0.892 -0.491 0.565
x 2.2226 0.436 5.095 0.000 1.368 3.078
" 285 | ], 286 | "text/plain": [ 287 | "\n", 288 | "\"\"\"\n", 289 | " Logit Regression Results \n", 290 | "==============================================================================\n", 291 | "Dep. Variable: y No. Observations: 100\n", 292 | "Model: Logit Df Residuals: 98\n", 293 | "Method: MLE Df Model: 1\n", 294 | "Date: Wed, 30 Sep 2020 Pseudo R-squ.: 0.3827\n", 295 | "Time: 02:50:12 Log-Likelihood: -42.785\n", 296 | "converged: True LL-Null: -69.315\n", 297 | "Covariance Type: nonrobust LLR p-value: 3.238e-13\n", 298 | "==============================================================================\n", 299 | " coef std err z P>|z| [0.025 0.975]\n", 300 | "------------------------------------------------------------------------------\n", 301 | "Intercept 0.0367 0.269 0.136 0.892 -0.491 0.565\n", 302 | "x 2.2226 0.436 5.095 0.000 1.368 3.078\n", 303 | "==============================================================================\n", 304 | "\"\"\"" 305 | ] 306 | }, 307 | "metadata": { 308 | "tags": [] 309 | }, 310 | "execution_count": 114 311 | } 312 | ] 313 | }, 314 | { 315 | "cell_type": "code", 316 | "metadata": { 317 | "id": "F6gUNlf6LbJc" 318 | }, 319 | "source": [ 320 | "# The in sample predictions\n", 321 | "yhat = 1 / (1 + np.exp(-fit.fittedvalues))" 322 | ], 323 | "execution_count": 115, 324 | "outputs": [] 325 | }, 326 | { 327 | "cell_type": "code", 328 | "metadata": { 329 | "id": "9LZ4MgGEPxEN", 330 | "outputId": "6fe594a1-85f9-4644-f41c-6991e120e91c", 331 | "colab": { 332 | "base_uri": "https://localhost:8080/", 333 | "height": 34 334 | } 335 | }, 336 | "source": [ 337 | "n = dat.shape[0]\n", 338 | "\n", 339 | "## Get the y and x from \n", 340 | "xtraining = torch.from_numpy(dat['x'].values)\n", 341 | "ytraining = torch.from_numpy(dat['y'].values)\n", 342 | "\n", 343 | "## PT wants floats\n", 344 | "xtraining = xtraining.float()\n", 345 | "ytraining = ytraining.float()\n", 346 | "\n", 347 | "## Dimension is 1xn not nx1\n", 348 | "## squeeze the second dimension\n", 349 | "xtraining = xtraining.unsqueeze(1)\n", 350 | "ytraining = ytraining.unsqueeze(1)\n", 351 | "\n", 352 | "## Show that everything is the right size\n", 353 | "[xtraining.shape, \n", 354 | " ytraining.shape,\n", 355 | " [n, 1]\n", 356 | " ]\n", 357 | "\n" 358 | ], 359 | "execution_count": 116, 360 | "outputs": [ 361 | { 362 | "output_type": "execute_result", 363 | "data": { 364 | "text/plain": [ 365 | "[torch.Size([100, 1]), torch.Size([100, 1]), [100, 1]]" 366 | ] 367 | }, 368 | "metadata": { 369 | "tags": [] 370 | }, 371 | "execution_count": 116 372 | } 373 | ] 374 | }, 375 | { 376 | "cell_type": "code", 377 | "metadata": { 378 | "id": "OZKrXwTjPdrB" 379 | }, 380 | "source": [ 381 | "## Doing it more now the pytorch docs recommend\n", 382 | "## Example taken from \n", 383 | "## https://medium.com/biaslyai/pytorch-linear-and-logistic-regression-models-5c5f0da2cb9\n", 384 | "\n", 385 | "## They recommend creating a class that defines\n", 386 | "## the model\n", 387 | "class LogisticRegression(torch.nn.Module):\n", 388 | " def __init__(self):\n", 389 | " super(LogisticRegression, self).__init__()\n", 390 | " self.linear = torch.nn.Linear(1, 1, bias = True)\n", 391 | " def forward(self, x):\n", 392 | " y_pred = torch.sigmoid(self.linear(x))\n", 393 | " return y_pred\n", 394 | "\n", 395 | "## Then the model is simply \n", 396 | "model = LogisticRegression()\n", 397 | "\n", 398 | "## MSE is the loss function\n", 399 | "loss_fn = torch.nn.BCELoss() \n", 400 | "\n", 401 | "## Set the optimizer\n", 402 | "optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)\n", 403 | "\n", 404 | "## Loop over iterations\n", 405 | "for t in range(100000):\n", 406 | "\n", 407 | " ## Forward propagation\n", 408 | " y_pred = model(xtraining)\n", 409 | "\n", 410 | " ## the loss for this interation\n", 411 | " loss = loss_fn(y_pred, ytraining)\n", 412 | "\n", 413 | " #print(t, loss.item() / n)\n", 414 | "\n", 415 | " ## Zero out the gradients before adding them up \n", 416 | " optimizer.zero_grad()\n", 417 | " \n", 418 | " ## Backprop\n", 419 | " loss.backward()\n", 420 | " \n", 421 | " ## Optimization step\n", 422 | " optimizer.step()\n", 423 | "\n" 424 | ], 425 | "execution_count": 117, 426 | "outputs": [] 427 | }, 428 | { 429 | "cell_type": "code", 430 | "metadata": { 431 | "id": "fd1wjXgukgqs", 432 | "outputId": "91f22597-1686-4b25-ee01-67dcba4753ca", 433 | "colab": { 434 | "base_uri": "https://localhost:8080/", 435 | "height": 282 436 | } 437 | }, 438 | "source": [ 439 | "ytest = model(xtraining)\n", 440 | "ytest = ytest.detach().numpy().reshape(-1)\n", 441 | "plt.plot(yhat, ytest, \".\")\n", 442 | "plt.plot([0, 1], [0, 1], linewidth=2)" 443 | ], 444 | "execution_count": 118, 445 | "outputs": [ 446 | { 447 | "output_type": "execute_result", 448 | "data": { 449 | "text/plain": [ 450 | "[]" 451 | ] 452 | }, 453 | "metadata": { 454 | "tags": [] 455 | }, 456 | "execution_count": 118 457 | }, 458 | { 459 | "output_type": "display_data", 460 | "data": { 461 | "image/png": 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\n", 462 | "text/plain": [ 463 | "
" 464 | ] 465 | }, 466 | "metadata": { 467 | "tags": [], 468 | "needs_background": "light" 469 | } 470 | } 471 | ] 472 | }, 473 | { 474 | "cell_type": "code", 475 | "metadata": { 476 | "id": "hZpPdBPYy53z", 477 | "outputId": "8ee26a76-37fd-4dc4-ea84-9a7f17cd5c3a", 478 | "colab": { 479 | "base_uri": "https://localhost:8080/", 480 | "height": 52 481 | } 482 | }, 483 | "source": [ 484 | "for param in model.parameters(): \n", 485 | " print(param.data)\n" 486 | ], 487 | "execution_count": 119, 488 | "outputs": [ 489 | { 490 | "output_type": "stream", 491 | "text": [ 492 | "tensor([[1.4062]])\n", 493 | "tensor([-0.0502])\n" 494 | ], 495 | "name": "stdout" 496 | } 497 | ] 498 | } 499 | ] 500 | } -------------------------------------------------------------------------------- /notebooks/multivariable_nn_in_torch.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "multivariable_nn_in_torch", 7 | "provenance": [], 8 | "collapsed_sections": [], 9 | "machine_shape": "hm", 10 | "include_colab_link": true 11 | }, 12 | "kernelspec": { 13 | "name": "python3", 14 | "display_name": "Python 3" 15 | } 16 | }, 17 | "cells": [ 18 | { 19 | "cell_type": "markdown", 20 | "metadata": { 21 | "id": "view-in-github", 22 | "colab_type": "text" 23 | }, 24 | "source": [ 25 | "\"Open" 26 | ] 27 | }, 28 | { 29 | "cell_type": "markdown", 30 | "metadata": { 31 | "id": "uiVM4lOtpJVt" 32 | }, 33 | "source": [ 34 | "This is an extension of using pytorch to perform a simple neural network. Note since this dataset is really small. I'm not splitting into a testing and training sets." 35 | ] 36 | }, 37 | { 38 | "cell_type": "code", 39 | "metadata": { 40 | "id": "6nKZWgTDvTTK", 41 | "outputId": "c31668c8-f0f9-4a36-a55b-476e20d04373", 42 | "colab": { 43 | "base_uri": "https://localhost:8080/", 44 | "height": 195 45 | } 46 | }, 47 | "source": [ 48 | "import pandas as pd\n", 49 | "import torch\n", 50 | "import matplotlib.pyplot as plt\n", 51 | "import numpy as np\n", 52 | "from sklearn.linear_model import LinearRegression\n", 53 | "\n", 54 | "## Read in the data\n", 55 | "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")\n", 56 | "\n", 57 | "def normalize(x):\n", 58 | " return (x - np.mean(x)) / np.std(x)\n", 59 | "\n", 60 | "## Create x variables that are normalized\n", 61 | "dat = dat.assign(\n", 62 | " y = dat.PD,\n", 63 | " x1 = normalize(dat.FLAIR),\n", 64 | " x2 = normalize(dat.T1), \n", 65 | " x3 = normalize(dat.T2),\n", 66 | " x4 = normalize(dat.FLAIR_10),\n", 67 | " x5 = normalize(dat.T1_10),\n", 68 | " x6 = normalize(dat.T2_10))\n", 69 | "dat = dat.filter(['y', 'x1', 'x2', 'x3', 'x4', 'x5', 'x6'], axis = 1)\n", 70 | "dat.head()" 71 | ], 72 | "execution_count": 7, 73 | "outputs": [ 74 | { 75 | "output_type": "execute_result", 76 | "data": { 77 | "text/html": [ 78 | "
\n", 79 | "\n", 92 | "\n", 93 | " \n", 94 | " \n", 95 | " \n", 96 | " \n", 97 | " \n", 98 | " \n", 99 | " \n", 100 | " \n", 101 | " \n", 102 | " \n", 103 | " \n", 104 | " \n", 105 | " \n", 106 | " \n", 107 | " \n", 108 | " \n", 109 | " \n", 110 | " \n", 111 | " \n", 112 | " \n", 113 | " \n", 114 | " \n", 115 | " \n", 116 | " \n", 117 | " \n", 118 | " \n", 119 | " \n", 120 | " \n", 121 | " \n", 122 | " \n", 123 | " \n", 124 | " \n", 125 | " \n", 126 | " \n", 127 | " \n", 128 | " \n", 129 | " \n", 130 | " \n", 131 | " \n", 132 | " \n", 133 | " \n", 134 | " \n", 135 | " \n", 136 | " \n", 137 | " \n", 138 | " \n", 139 | " \n", 140 | " \n", 141 | " \n", 142 | " \n", 143 | " \n", 144 | " \n", 145 | " \n", 146 | " \n", 147 | " \n", 148 | " \n", 149 | " \n", 150 | " \n", 151 | " \n", 152 | " \n", 153 | " \n", 154 | " \n", 155 | " \n", 156 | " \n", 157 | "
yx1x2x3x4x5x6
01.586219-0.841279-0.9041281.4663530.556695-0.5692181.921010
11.766672-0.049795-1.5011280.5341211.403361-1.8113741.800152
20.262042-1.008629-0.981815-0.746050-1.252711-0.519458-1.307041
30.011104-1.006151-1.471756-1.284565-1.138899-1.733044-1.174082
41.730152-0.161726-0.9849700.9580991.234082-0.8586391.184153
\n", 158 | "
" 159 | ], 160 | "text/plain": [ 161 | " y x1 x2 x3 x4 x5 x6\n", 162 | "0 1.586219 -0.841279 -0.904128 1.466353 0.556695 -0.569218 1.921010\n", 163 | "1 1.766672 -0.049795 -1.501128 0.534121 1.403361 -1.811374 1.800152\n", 164 | "2 0.262042 -1.008629 -0.981815 -0.746050 -1.252711 -0.519458 -1.307041\n", 165 | "3 0.011104 -1.006151 -1.471756 -1.284565 -1.138899 -1.733044 -1.174082\n", 166 | "4 1.730152 -0.161726 -0.984970 0.958099 1.234082 -0.858639 1.184153" 167 | ] 168 | }, 169 | "metadata": { 170 | "tags": [] 171 | }, 172 | "execution_count": 7 173 | } 174 | ] 175 | }, 176 | { 177 | "cell_type": "code", 178 | "metadata": { 179 | "id": "KlKINCcFrw_D" 180 | }, 181 | "source": [ 182 | "y = dat.y\n", 183 | "x = dat.drop('y', axis = 1)\n", 184 | "\n", 185 | "## I find it easier to convert to np arrays before torch tensors\n", 186 | "y = pd.DataFrame.to_numpy(y)\n", 187 | "x = pd.DataFrame.to_numpy(x)\n", 188 | "\n", 189 | "## This will give you a sense of the\n", 190 | "## in sample prediction using just a linear model\n", 191 | "#reg = LinearRegression().fit(x, y)\n", 192 | "#yhat = reg.predict(x)\n", 193 | "#plt.plot(y, yhat, \".\")\n", 194 | "\n", 195 | "## have to switch floating point precision for torch\n", 196 | "xtraining = torch.from_numpy(x).float()\n", 197 | "ytraining = torch.from_numpy(y).float()" 198 | ], 199 | "execution_count": 8, 200 | "outputs": [] 201 | }, 202 | { 203 | "cell_type": "code", 204 | "metadata": { 205 | "id": "9LZ4MgGEPxEN", 206 | "outputId": "8342769b-4398-4f06-b503-6b8fa114013b", 207 | "colab": { 208 | "base_uri": "https://localhost:8080/", 209 | "height": 34 210 | } 211 | }, 212 | "source": [ 213 | "n = x.shape[0]\n", 214 | "p = x.shape[1]\n", 215 | "\n", 216 | "## Show that everything is the right size\n", 217 | "print([xtraining.shape, ytraining.shape, [n, p]])" 218 | ], 219 | "execution_count": 10, 220 | "outputs": [ 221 | { 222 | "output_type": "stream", 223 | "text": [ 224 | "[torch.Size([100, 6]), torch.Size([100]), [100, 6]]\n" 225 | ], 226 | "name": "stdout" 227 | } 228 | ] 229 | }, 230 | { 231 | "cell_type": "code", 232 | "metadata": { 233 | "id": "CnbdQ-kP4c5u" 234 | }, 235 | "source": [ 236 | "## Two layers\n", 237 | "model = torch.nn.Sequential(\n", 238 | " torch.nn.Linear(p,3),\n", 239 | " torch.nn.ReLU(),\n", 240 | " torch.nn.Linear(3,1)\n", 241 | ")\n", 242 | "\n", 243 | "## MSE is the loss function\n", 244 | "loss_fn = torch.nn.MSELoss(reduction='sum') \n", 245 | "\n", 246 | "## Set the optimizer\n", 247 | "#optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)\n", 248 | "optimizer = torch.optim.Adam(model.parameters())\n", 249 | "\n" 250 | ], 251 | "execution_count": 11, 252 | "outputs": [] 253 | }, 254 | { 255 | "cell_type": "code", 256 | "metadata": { 257 | "id": "OZKrXwTjPdrB", 258 | "outputId": "059251fe-8512-4e0e-d05c-8128b2c96a7e", 259 | "colab": { 260 | "base_uri": "https://localhost:8080/", 261 | "height": 72 262 | } 263 | }, 264 | "source": [ 265 | "## Loop over iterations\n", 266 | "for t in range(100000):\n", 267 | "\n", 268 | " ## Forward propagation\n", 269 | " y_pred = model(xtraining)\n", 270 | "\n", 271 | " ## the loss for this interation\n", 272 | " loss = loss_fn(y_pred, ytraining)\n", 273 | "\n", 274 | " ## Zero out the gradients before adding them up \n", 275 | " optimizer.zero_grad()\n", 276 | " \n", 277 | " ## Backprop\n", 278 | " loss.backward()\n", 279 | " \n", 280 | " ## Optimization step\n", 281 | " optimizer.step()\n", 282 | "\n" 283 | ], 284 | "execution_count": 12, 285 | "outputs": [ 286 | { 287 | "output_type": "stream", 288 | "text": [ 289 | "/usr/local/lib/python3.6/dist-packages/torch/nn/modules/loss.py:445: UserWarning: Using a target size (torch.Size([100])) that is different to the input size (torch.Size([100, 1])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n", 290 | " return F.mse_loss(input, target, reduction=self.reduction)\n" 291 | ], 292 | "name": "stderr" 293 | } 294 | ] 295 | }, 296 | { 297 | "cell_type": "code", 298 | "metadata": { 299 | "id": "fd1wjXgukgqs", 300 | "outputId": "6d32f7bc-4d14-4f77-e0f6-f754a0662944", 301 | "colab": { 302 | "base_uri": "https://localhost:8080/", 303 | "height": 282 304 | } 305 | }, 306 | "source": [ 307 | "#How are we doing in sample?\n", 308 | "yhat = model(xtraining).detach().numpy().reshape(-1)\n", 309 | "plt.plot(ytraining, yhat, \".\") " 310 | ], 311 | "execution_count": 13, 312 | "outputs": [ 313 | { 314 | "output_type": "execute_result", 315 | "data": { 316 | "text/plain": [ 317 | "[]" 318 | ] 319 | }, 320 | "metadata": { 321 | "tags": [] 322 | }, 323 | "execution_count": 13 324 | }, 325 | { 326 | "output_type": "display_data", 327 | "data": { 328 | "image/png": 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329 | "text/plain": [ 330 | "
" 331 | ] 332 | }, 333 | "metadata": { 334 | "tags": [], 335 | "needs_background": "light" 336 | } 337 | } 338 | ] 339 | } 340 | ] 341 | } -------------------------------------------------------------------------------- /notebooks/notebook5_a.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "notebook5.a.ipynb", 7 | "provenance": [], 8 | "include_colab_link": true 9 | }, 10 | "kernelspec": { 11 | "name": "python3", 12 | "display_name": "Python 3" 13 | } 14 | }, 15 | "cells": [ 16 | { 17 | "cell_type": "markdown", 18 | "metadata": { 19 | "id": "view-in-github", 20 | "colab_type": "text" 21 | }, 22 | "source": [ 23 | "\"Open" 24 | ] 25 | }, 26 | { 27 | "cell_type": "code", 28 | "metadata": { 29 | "id": "GMMLqAkYRxb5", 30 | "colab_type": "code", 31 | "colab": {} 32 | }, 33 | "source": [ 34 | "import numpy as np\n", 35 | "import pandas as pd\n", 36 | "import seaborn as sns\n", 37 | "import matplotlib.pyplot as plt\n", 38 | "import sklearn.linear_model as lm\n", 39 | "import sklearn as skl\n", 40 | "import statsmodels.formula.api as smf\n", 41 | "import statsmodels as sm\n", 42 | "\n", 43 | "## this sets some style parameters\n", 44 | "sns.set()\n", 45 | "\n", 46 | "## Read in the data and display a few rows\n", 47 | "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")" 48 | ], 49 | "execution_count": 14, 50 | "outputs": [] 51 | }, 52 | { 53 | "cell_type": "code", 54 | "metadata": { 55 | "id": "K8Yp-vpBC2Yh", 56 | "colab_type": "code", 57 | "colab": { 58 | "base_uri": "https://localhost:8080/", 59 | "height": 195 60 | }, 61 | "outputId": "19a8f4f8-2072-4df4-d757-f11c92f42c90" 62 | }, 63 | "source": [ 64 | "dat.head()" 65 | ], 66 | "execution_count": 15, 67 | "outputs": [ 68 | { 69 | "output_type": "execute_result", 70 | "data": { 71 | "text/html": [ 72 | "
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FLAIRPDT1T2FLAIR_10PD_10T1_10T2_10FLAIR_20PD_20T1_20T2_20GOLD_Lesions
01.1436921.586219-0.7998591.6344670.4375680.823800-0.0020590.5736630.2798320.5483410.2191360.2986620
11.6525521.766672-1.2509920.9212300.6630370.880250-0.4220600.5425970.4221820.5497110.0615730.2809720
21.0360990.262042-0.858565-0.058211-0.044280-0.3085690.014766-0.256075-0.136532-0.3509050.020673-0.2599140
31.0376920.011104-1.228796-0.470222-0.013971-0.000498-0.395575-0.2219000.000807-0.003085-0.193249-0.1392840
41.5805891.730152-0.8609491.2456090.6179570.866352-0.0999190.3842610.3911330.6088260.0716480.3406010
\n", 188 | "
" 189 | ], 190 | "text/plain": [ 191 | " FLAIR PD T1 ... T1_20 T2_20 GOLD_Lesions\n", 192 | "0 1.143692 1.586219 -0.799859 ... 0.219136 0.298662 0\n", 193 | "1 1.652552 1.766672 -1.250992 ... 0.061573 0.280972 0\n", 194 | "2 1.036099 0.262042 -0.858565 ... 0.020673 -0.259914 0\n", 195 | "3 1.037692 0.011104 -1.228796 ... -0.193249 -0.139284 0\n", 196 | "4 1.580589 1.730152 -0.860949 ... 0.071648 0.340601 0\n", 197 | "\n", 198 | "[5 rows x 13 columns]" 199 | ] 200 | }, 201 | "metadata": { 202 | "tags": [] 203 | }, 204 | "execution_count": 15 205 | } 206 | ] 207 | }, 208 | { 209 | "cell_type": "code", 210 | "metadata": { 211 | "id": "fDJOnSsxe2N5", 212 | "colab_type": "code", 213 | "colab": { 214 | "base_uri": "https://localhost:8080/", 215 | "height": 404 216 | }, 217 | "outputId": "07acb08e-572d-4318-85b2-b59099335efb" 218 | }, 219 | "source": [ 220 | "#results = smf.ols('PD ~ FLAIR + T1 + T2 + FLAIR_10 + T1_10 + T2_10 + FLAIR_20', data = dat).fit()\n", 221 | "results = smf.ols('PD ~ FLAIR + T1', data = dat).fit()\n", 222 | "print(results.summary2())\n" 223 | ], 224 | "execution_count": 19, 225 | "outputs": [ 226 | { 227 | "output_type": "stream", 228 | "text": [ 229 | " Results: Ordinary least squares\n", 230 | "=================================================================\n", 231 | "Model: OLS Adj. R-squared: 0.368 \n", 232 | "Dependent Variable: PD AIC: 180.8632\n", 233 | "Date: 2020-09-20 19:46 BIC: 188.6787\n", 234 | "No. Observations: 100 Log-Likelihood: -87.432 \n", 235 | "Df Model: 2 F-statistic: 29.82 \n", 236 | "Df Residuals: 97 Prob (F-statistic): 8.04e-11\n", 237 | "R-squared: 0.381 Scale: 0.34688 \n", 238 | "------------------------------------------------------------------\n", 239 | " Coef. Std.Err. t P>|t| [0.025 0.975]\n", 240 | "------------------------------------------------------------------\n", 241 | "Intercept 0.0718 0.1658 0.4333 0.6657 -0.2572 0.4009\n", 242 | "FLAIR 0.3448 0.0917 3.7621 0.0003 0.1629 0.5267\n", 243 | "T1 -0.5354 0.0780 -6.8662 0.0000 -0.6902 -0.3807\n", 244 | "-----------------------------------------------------------------\n", 245 | "Omnibus: 6.896 Durbin-Watson: 2.127\n", 246 | "Prob(Omnibus): 0.032 Jarque-Bera (JB): 7.092\n", 247 | "Skew: -0.443 Prob(JB): 0.029\n", 248 | "Kurtosis: 3.958 Condition No.: 6 \n", 249 | "=================================================================\n", 250 | "\n" 251 | ], 252 | "name": "stdout" 253 | } 254 | ] 255 | }, 256 | { 257 | "cell_type": "code", 258 | "metadata": { 259 | "id": "uxE_9nEIA3mE", 260 | "colab_type": "code", 261 | "colab": { 262 | "base_uri": "https://localhost:8080/", 263 | "height": 34 264 | }, 265 | "outputId": "5dc9c314-aeb9-4ca0-aa3b-dc2230580849" 266 | }, 267 | "source": [ 268 | "y1 = dat.PD\n", 269 | "x1 = np.zeros(y.size) + 1\n", 270 | "x2 = dat.FLAIR\n", 271 | "x3 = dat.T1\n", 272 | "\n", 273 | "def resid(x, y):\n", 274 | " return y - x * np.sum(x * y) / np.sum(x ** 2)\n", 275 | "\n", 276 | "## Regress x1 out of everything\n", 277 | "ey1x1 = resid(x1, y1)\n", 278 | "ex2x1 = resid(x1, x2)\n", 279 | "ex3x1 = resid(x1, x3)\n", 280 | "\n", 281 | "## Regress the residual for x2 out of everything\n", 282 | "ey1x1x2 = resid(ex2x1, ey1x1)\n", 283 | "ex3x1x2 = resid(ex2x1, ex3x1)\n", 284 | "\n", 285 | "\n", 286 | "np.sum(ex3x1x2 * ey1x1x2) / np.sum(ex3x1x2 ** 2)\n", 287 | "\n" 288 | ], 289 | "execution_count": 20, 290 | "outputs": [ 291 | { 292 | "output_type": "execute_result", 293 | "data": { 294 | "text/plain": [ 295 | "-0.5354478184289665" 296 | ] 297 | }, 298 | "metadata": { 299 | "tags": [] 300 | }, 301 | "execution_count": 20 302 | } 303 | ] 304 | } 305 | ] 306 | } -------------------------------------------------------------------------------- /notebooks/notebook6.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "notebook6.ipynb", 7 | "provenance": [], 8 | "collapsed_sections": [], 9 | "include_colab_link": true 10 | }, 11 | "kernelspec": { 12 | "name": "python3", 13 | "display_name": "Python 3" 14 | } 15 | }, 16 | "cells": [ 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "id": "view-in-github", 21 | "colab_type": "text" 22 | }, 23 | "source": [ 24 | "\"Open" 25 | ] 26 | }, 27 | { 28 | "cell_type": "markdown", 29 | "metadata": { 30 | "id": "QliNPatWGeQF", 31 | "colab_type": "text" 32 | }, 33 | "source": [ 34 | "This example from the pytorch documentation [here](https://pytorch.org/tutorials/beginner/pytorch_with_examples.html) displays generating random y ad x dat and fitting a multi-layer neural network." 35 | ] 36 | }, 37 | { 38 | "cell_type": "code", 39 | "metadata": { 40 | "id": "54gmWH2_GILQ", 41 | "colab_type": "code", 42 | "outputId": "460f97b3-7974-484e-9ad5-428fb776b4e8", 43 | "colab": { 44 | "base_uri": "https://localhost:8080/", 45 | "height": 108 46 | } 47 | }, 48 | "source": [ 49 | "# -*- coding: utf-8 -*-\n", 50 | "import torch\n", 51 | "\n", 52 | "# N is batch size; D_in is input dimension;\n", 53 | "# H is hidden dimension; D_out is output dimension.\n", 54 | "N, D_in, H, D_out = 64, 1000, 100, 10\n", 55 | "\n", 56 | "# Create random Tensors to hold inputs and outputs\n", 57 | "x = torch.randn(N, D_in)\n", 58 | "y = torch.randn(N, D_out)\n", 59 | "\n", 60 | "# Use the nn package to define our model as a sequence of layers. nn.Sequential\n", 61 | "# is a Module which contains other Modules, and applies them in sequence to\n", 62 | "# produce its output. Each Linear Module computes output from input using a\n", 63 | "# linear function, and holds internal Tensors for its weight and bias.\n", 64 | "model = torch.nn.Sequential(\n", 65 | " torch.nn.Linear(D_in, H),\n", 66 | " torch.nn.ReLU(),\n", 67 | " torch.nn.Linear(H, D_out),\n", 68 | ")\n", 69 | "\n", 70 | "# The nn package also contains definitions of popular loss functions; in this\n", 71 | "# case we will use Mean Squared Error (MSE) as our loss function.\n", 72 | "loss_fn = torch.nn.MSELoss(reduction='sum')\n", 73 | "\n", 74 | "learning_rate = 1e-4\n", 75 | "for t in range(500):\n", 76 | " # Forward pass: compute predicted y by passing x to the model. Module objects\n", 77 | " # override the __call__ operator so you can call them like functions. When\n", 78 | " # doing so you pass a Tensor of input data to the Module and it produces\n", 79 | " # a Tensor of output data.\n", 80 | " y_pred = model(x)\n", 81 | "\n", 82 | " # Compute and print loss. We pass Tensors containing the predicted and true\n", 83 | " # values of y, and the loss function returns a Tensor containing the\n", 84 | " # loss.\n", 85 | " loss = loss_fn(y_pred, y)\n", 86 | " if t % 100 == 99:\n", 87 | " print(t, loss.item())\n", 88 | "\n", 89 | " # Zero the gradients before running the backward pass.\n", 90 | " model.zero_grad()\n", 91 | "\n", 92 | " # Backward pass: compute gradient of the loss with respect to all the learnable\n", 93 | " # parameters of the model. Internally, the parameters of each Module are stored\n", 94 | " # in Tensors with requires_grad=True, so this call will compute gradients for\n", 95 | " # all learnable parameters in the model.\n", 96 | " loss.backward()\n", 97 | "\n", 98 | " # Update the weights using gradient descent. Each parameter is a Tensor, so\n", 99 | " # we can access its gradients like we did before.\n", 100 | " with torch.no_grad():\n", 101 | " for param in model.parameters():\n", 102 | " param -= learning_rate * param.grad" 103 | ], 104 | "execution_count": 129, 105 | "outputs": [ 106 | { 107 | "output_type": "stream", 108 | "text": [ 109 | "99 1.9933761358261108\n", 110 | "199 0.020633060485124588\n", 111 | "299 0.00045402691466733813\n", 112 | "399 1.4306728189694695e-05\n", 113 | "499 5.802120313092018e-07\n" 114 | ], 115 | "name": "stdout" 116 | } 117 | ] 118 | }, 119 | { 120 | "cell_type": "markdown", 121 | "metadata": { 122 | "id": "qWcVUq9RGxTB", 123 | "colab_type": "text" 124 | }, 125 | "source": [ 126 | "Let's update that example for our setting using the voxel level data." 127 | ] 128 | }, 129 | { 130 | "cell_type": "code", 131 | "metadata": { 132 | "id": "62iyChkPGwZD", 133 | "colab_type": "code", 134 | "colab": {} 135 | }, 136 | "source": [ 137 | "import torch\n", 138 | "import numpy as np\n", 139 | "import pandas as pd\n", 140 | "import seaborn as sns\n", 141 | "import matplotlib.pyplot as plt\n", 142 | "import sklearn.linear_model as lm\n", 143 | "## this sets some style parameters\n", 144 | "sns.set()\n", 145 | "\n", 146 | "## Download in the data if it's not already there\n", 147 | "! if [ ! -e oasis.csv ]; \\\n", 148 | " then wget https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv; \\\n", 149 | "fi;\n", 150 | "\n", 151 | "## Read in the data and display a few rows\n", 152 | "dat = pd.read_csv(\"oasis.csv\")" 153 | ], 154 | "execution_count": 0, 155 | "outputs": [] 156 | }, 157 | { 158 | "cell_type": "code", 159 | "metadata": { 160 | "id": "neIwiOlRTIor", 161 | "colab_type": "code", 162 | "colab": {} 163 | }, 164 | "source": [ 165 | "trainFraction = .75\n", 166 | "\n", 167 | "sample = np.random.uniform(size = 100) < trainFraction\n", 168 | "trainingDat = dat[sample]\n", 169 | "testingDat = dat[~sample]\n" 170 | ], 171 | "execution_count": 0, 172 | "outputs": [] 173 | }, 174 | { 175 | "cell_type": "code", 176 | "metadata": { 177 | "id": "-tVT-AsOTPgN", 178 | "colab_type": "code", 179 | "colab": { 180 | "base_uri": "https://localhost:8080/", 181 | "height": 89 182 | }, 183 | "outputId": "1f938b04-48b9-4fa2-8b94-160c233b8a7e" 184 | }, 185 | "source": [ 186 | "x = torch.from_numpy(dat[['PD','T1', 'T2', 'FLAIR_10', 'T1_10', 'T2_10', 'FLAIR_20']].values)\n", 187 | "y = torch.from_numpy(dat[['FLAIR']].values)\n", 188 | "\n", 189 | "##pytorch wants type as float\n", 190 | "x = x.float()\n", 191 | "y = y.float()\n", 192 | "\n", 193 | "xtraining = x[sample]\n", 194 | "xtesting = x[~sample]\n", 195 | "ytraining = y[sample]\n", 196 | "ytesting = y[~sample]\n", 197 | "\n", 198 | "[\n", 199 | " xtraining.size(),\n", 200 | " ytraining.size(),\n", 201 | " xtesting.size(),\n", 202 | " ytesting.size(),\n", 203 | "]\n" 204 | ], 205 | "execution_count": 4, 206 | "outputs": [ 207 | { 208 | "output_type": "execute_result", 209 | "data": { 210 | "text/plain": [ 211 | "[torch.Size([75, 7]),\n", 212 | " torch.Size([75, 1]),\n", 213 | " torch.Size([25, 7]),\n", 214 | " torch.Size([25, 1])]" 215 | ] 216 | }, 217 | "metadata": { 218 | "tags": [] 219 | }, 220 | "execution_count": 4 221 | } 222 | ] 223 | }, 224 | { 225 | "cell_type": "code", 226 | "metadata": { 227 | "id": "D2UxGTdkaBdO", 228 | "colab_type": "code", 229 | "colab": {} 230 | }, 231 | "source": [ 232 | "## Define the model\n", 233 | "## Dimension of the hidden layer\n", 234 | "H = 10\n", 235 | "\n", 236 | "## Number of predictors\n", 237 | "D_in = xtraining.size()[1]\n", 238 | "D_out = 1\n", 239 | "\n", 240 | "model = torch.nn.Sequential(\n", 241 | " torch.nn.Linear(D_in, H),\n", 242 | " torch.nn.ReLU(),\n", 243 | " torch.nn.Linear(H, D_out),\n", 244 | ")\n", 245 | "\n" 246 | ], 247 | "execution_count": 0, 248 | "outputs": [] 249 | }, 250 | { 251 | "cell_type": "code", 252 | "metadata": { 253 | "id": "lnoPaqh7Rm2M", 254 | "colab_type": "code", 255 | "colab": { 256 | "base_uri": "https://localhost:8080/", 257 | "height": 108 258 | }, 259 | "outputId": "9067a2a4-7d16-4efa-8ee0-8ef8d44db9d2" 260 | }, 261 | "source": [ 262 | "loss_fn = torch.nn.MSELoss(reduction='sum')\n", 263 | "\n", 264 | "learning_rate = 1e-4\n", 265 | "for t in range(500):\n", 266 | " y_pred = model(xtraining)\n", 267 | " loss = loss_fn(y_pred, ytraining)\n", 268 | " if t % 100 == 99:\n", 269 | " print(t, loss.item())\n", 270 | " model.zero_grad()\n", 271 | " loss.backward()\n", 272 | " with torch.no_grad():\n", 273 | " for param in model.parameters():\n", 274 | " param -= learning_rate * param.grad\n" 275 | ], 276 | "execution_count": 6, 277 | "outputs": [ 278 | { 279 | "output_type": "stream", 280 | "text": [ 281 | "99 31.615375518798828\n", 282 | "199 28.612531661987305\n", 283 | "299 27.466083526611328\n", 284 | "399 26.587757110595703\n", 285 | "499 25.88320541381836\n" 286 | ], 287 | "name": "stdout" 288 | } 289 | ] 290 | }, 291 | { 292 | "cell_type": "code", 293 | "metadata": { 294 | "id": "eZswhY21bcwK", 295 | "colab_type": "code", 296 | "outputId": "bbefd7ef-cf11-4bd1-9ffc-7e99344e2755", 297 | "colab": { 298 | "base_uri": "https://localhost:8080/", 299 | "height": 292 300 | } 301 | }, 302 | "source": [ 303 | "## try prediction\n", 304 | "ytesting_pred = model(xtesting)\n", 305 | "a = ytesting_pred.detach().numpy()\n", 306 | "\n", 307 | "plt.scatter(a[:,0], ytesting[:,0])" 308 | ], 309 | "execution_count": 7, 310 | "outputs": [ 311 | { 312 | "output_type": "execute_result", 313 | "data": { 314 | "text/plain": [ 315 | "" 316 | ] 317 | }, 318 | "metadata": { 319 | "tags": [] 320 | }, 321 | "execution_count": 7 322 | }, 323 | { 324 | "output_type": "display_data", 325 | "data": { 326 | "image/png": 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327 | "text/plain": [ 328 | "
" 329 | ] 330 | }, 331 | "metadata": { 332 | "tags": [] 333 | } 334 | } 335 | ] 336 | } 337 | ] 338 | } -------------------------------------------------------------------------------- /notebooks/regression_examples.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "regression_examples", 7 | "provenance": [], 8 | "authorship_tag": "ABX9TyPD6YfE7eh7Lu8TLxXjNkFR", 9 | "include_colab_link": true 10 | }, 11 | "kernelspec": { 12 | "name": "python3", 13 | "display_name": "Python 3" 14 | } 15 | }, 16 | "cells": [ 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "id": "view-in-github", 21 | "colab_type": "text" 22 | }, 23 | "source": [ 24 | "\"Open" 25 | ] 26 | }, 27 | { 28 | "cell_type": "code", 29 | "metadata": { 30 | "id": "oIimJROu2Hc_", 31 | "colab_type": "code", 32 | "colab": {} 33 | }, 34 | "source": [ 35 | "import pandas as pd\n", 36 | "import numpy as np\n", 37 | "from sklearn.linear_model import LinearRegression\n", 38 | "import matplotlib.pyplot as plt\n" 39 | ], 40 | "execution_count": 43, 41 | "outputs": [] 42 | }, 43 | { 44 | "cell_type": "code", 45 | "metadata": { 46 | "id": "vsVJc6lS2Qov", 47 | "colab_type": "code", 48 | "colab": { 49 | "base_uri": "https://localhost:8080/", 50 | "height": 201 51 | }, 52 | "outputId": "fc0b2fe3-eccd-4f2a-819f-084bc8e2602d" 53 | }, 54 | "source": [ 55 | "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/swiss.csv\")\n", 56 | "dat.head()\n" 57 | ], 58 | "execution_count": 45, 59 | "outputs": [ 60 | { 61 | "output_type": "execute_result", 62 | "data": { 63 | "text/html": [ 64 | "
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RegionFertilityAgricultureExaminationEducationCatholicInfant.Mortality
0Courtelary80.217.015129.9622.2
1Delemont83.145.16984.8422.2
2Franches-Mnt92.539.75593.4020.2
3Moutier85.836.512733.7720.3
4Neuveville76.943.517155.1620.6
\n", 144 | "
" 145 | ], 146 | "text/plain": [ 147 | " Region Fertility Agriculture ... Education Catholic Infant.Mortality\n", 148 | "0 Courtelary 80.2 17.0 ... 12 9.96 22.2\n", 149 | "1 Delemont 83.1 45.1 ... 9 84.84 22.2\n", 150 | "2 Franches-Mnt 92.5 39.7 ... 5 93.40 20.2\n", 151 | "3 Moutier 85.8 36.5 ... 7 33.77 20.3\n", 152 | "4 Neuveville 76.9 43.5 ... 15 5.16 20.6\n", 153 | "\n", 154 | "[5 rows x 7 columns]" 155 | ] 156 | }, 157 | "metadata": { 158 | "tags": [] 159 | }, 160 | "execution_count": 45 161 | } 162 | ] 163 | }, 164 | { 165 | "cell_type": "code", 166 | "metadata": { 167 | "id": "T34j2o8u2cH_", 168 | "colab_type": "code", 169 | "colab": { 170 | "base_uri": "https://localhost:8080/", 171 | "height": 54 172 | }, 173 | "outputId": "61309a3a-8ff6-489d-9dfd-c1ea40be99d8" 174 | }, 175 | "source": [ 176 | "y = dat.Fertility\n", 177 | "x = dat.drop(['Region', 'Fertility'], axis=1)\n", 178 | "fit = LinearRegression().fit(x, y)\n", 179 | "yhat = fit.predict(x)\n", 180 | "[fit.intercept_, fit.coef_]\n" 181 | ], 182 | "execution_count": 49, 183 | "outputs": [ 184 | { 185 | "output_type": "execute_result", 186 | "data": { 187 | "text/plain": [ 188 | "[66.91518167896871,\n", 189 | " array([-0.17211397, -0.25800824, -0.87094006, 0.10411533, 1.07704814])]" 190 | ] 191 | }, 192 | "metadata": { 193 | "tags": [] 194 | }, 195 | "execution_count": 49 196 | } 197 | ] 198 | }, 199 | { 200 | "cell_type": "code", 201 | "metadata": { 202 | "id": "Dwova9_d5BKe", 203 | "colab_type": "code", 204 | "colab": {} 205 | }, 206 | "source": [ 207 | "x2 = x\n", 208 | "x2['Test'] = x2.Agriculture + x2.Examination\n", 209 | "fit2 = LinearRegression().fit(x2, y)\n", 210 | "yhat2 = fit2.predict(x2)" 211 | ], 212 | "execution_count": 50, 213 | "outputs": [] 214 | }, 215 | { 216 | "cell_type": "code", 217 | "metadata": { 218 | "id": "RAIz1jJs6YFg", 219 | "colab_type": "code", 220 | "colab": { 221 | "base_uri": "https://localhost:8080/", 222 | "height": 283 223 | }, 224 | "outputId": "de9beb6e-d3e6-4033-eba9-27689bac6ff4" 225 | }, 226 | "source": [ 227 | "plt.plot(yhat, yhat2)" 228 | ], 229 | "execution_count": 51, 230 | "outputs": [ 231 | { 232 | "output_type": "execute_result", 233 | "data": { 234 | "text/plain": [ 235 | "[]" 236 | ] 237 | }, 238 | "metadata": { 239 | "tags": [] 240 | }, 241 | "execution_count": 51 242 | }, 243 | { 244 | "output_type": "display_data", 245 | "data": { 246 | "image/png": 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\n", 247 | "text/plain": [ 248 | "
" 249 | ] 250 | }, 251 | "metadata": { 252 | "tags": [], 253 | "needs_background": "light" 254 | } 255 | } 256 | ] 257 | }, 258 | { 259 | "cell_type": "code", 260 | "metadata": { 261 | "id": "626Z0Ql66qWx", 262 | "colab_type": "code", 263 | "colab": { 264 | "base_uri": "https://localhost:8080/", 265 | "height": 283 266 | }, 267 | "outputId": "12617691-af4e-47d3-d080-10223101ec81" 268 | }, 269 | "source": [ 270 | "x3 = x2.drop(['Agriculture'], axis = 1)\n", 271 | "fit3 = LinearRegression().fit(x3, y)\n", 272 | "yhat3 = fit3.predict(x3)\n", 273 | "plt.plot(yhat, yhat3)\n" 274 | ], 275 | "execution_count": 53, 276 | "outputs": [ 277 | { 278 | "output_type": "execute_result", 279 | "data": { 280 | "text/plain": [ 281 | "[]" 282 | ] 283 | }, 284 | "metadata": { 285 | "tags": [] 286 | }, 287 | "execution_count": 53 288 | }, 289 | { 290 | "output_type": "display_data", 291 | "data": { 292 | "image/png": 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\n", 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" 295 | ] 296 | }, 297 | "metadata": { 298 | "tags": [], 299 | "needs_background": "light" 300 | } 301 | } 302 | ] 303 | } 304 | ] 305 | } -------------------------------------------------------------------------------- /notebooks/regression_through_the_origin.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "Regression through the origin.ipynb", 7 | "provenance": [], 8 | "authorship_tag": "ABX9TyOKHYc47ZJyl0IPyt5p0mYA", 9 | "include_colab_link": true 10 | }, 11 | "kernelspec": { 12 | "name": "python3", 13 | "display_name": "Python 3" 14 | } 15 | }, 16 | "cells": [ 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "id": "view-in-github", 21 | "colab_type": "text" 22 | }, 23 | "source": [ 24 | "\"Open" 25 | ] 26 | }, 27 | { 28 | "cell_type": "code", 29 | "metadata": { 30 | "id": "SXdTawbDmq7p", 31 | "colab_type": "code", 32 | "colab": {} 33 | }, 34 | "source": [ 35 | "import pandas as pd\n", 36 | "import numpy as np\n", 37 | "import matplotlib.pyplot as plt\n" 38 | ], 39 | "execution_count": 20, 40 | "outputs": [] 41 | }, 42 | { 43 | "cell_type": "code", 44 | "metadata": { 45 | "id": "z_P87xbFm05p", 46 | "colab_type": "code", 47 | "colab": { 48 | "base_uri": "https://localhost:8080/", 49 | "height": 201 50 | }, 51 | "outputId": "a2b65327-5b42-4d24-b26a-4fd6c957f94c" 52 | }, 53 | "source": [ 54 | "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")\n", 55 | "dat.head()" 56 | ], 57 | "execution_count": 21, 58 | "outputs": [ 59 | { 60 | "output_type": "execute_result", 61 | "data": { 62 | "text/html": [ 63 | "
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FLAIRPDT1T2FLAIR_10PD_10T1_10T2_10FLAIR_20PD_20T1_20T2_20GOLD_Lesions
01.1436921.586219-0.7998591.6344670.4375680.823800-0.0020590.5736630.2798320.5483410.2191360.2986620
11.6525521.766672-1.2509920.9212300.6630370.880250-0.4220600.5425970.4221820.5497110.0615730.2809720
21.0360990.262042-0.858565-0.058211-0.044280-0.3085690.014766-0.256075-0.136532-0.3509050.020673-0.2599140
31.0376920.011104-1.228796-0.470222-0.013971-0.000498-0.395575-0.2219000.000807-0.003085-0.193249-0.1392840
41.5805891.730152-0.8609491.2456090.6179570.866352-0.0999190.3842610.3911330.6088260.0716480.3406010
\n", 179 | "
" 180 | ], 181 | "text/plain": [ 182 | " FLAIR PD T1 ... T1_20 T2_20 GOLD_Lesions\n", 183 | "0 1.143692 1.586219 -0.799859 ... 0.219136 0.298662 0\n", 184 | "1 1.652552 1.766672 -1.250992 ... 0.061573 0.280972 0\n", 185 | "2 1.036099 0.262042 -0.858565 ... 0.020673 -0.259914 0\n", 186 | "3 1.037692 0.011104 -1.228796 ... -0.193249 -0.139284 0\n", 187 | "4 1.580589 1.730152 -0.860949 ... 0.071648 0.340601 0\n", 188 | "\n", 189 | "[5 rows x 13 columns]" 190 | ] 191 | }, 192 | "metadata": { 193 | "tags": [] 194 | }, 195 | "execution_count": 21 196 | } 197 | ] 198 | }, 199 | { 200 | "cell_type": "code", 201 | "metadata": { 202 | "id": "YIWNN3y_nBmi", 203 | "colab_type": "code", 204 | "colab": { 205 | "base_uri": "https://localhost:8080/", 206 | "height": 283 207 | }, 208 | "outputId": "80b6c4d1-301f-46a2-c481-9c4ac2598881" 209 | }, 210 | "source": [ 211 | "x = dat.T2\n", 212 | "y = dat.PD\n", 213 | "plt.plot(x, y, 'o')" 214 | ], 215 | "execution_count": 25, 216 | "outputs": [ 217 | { 218 | "output_type": "execute_result", 219 | "data": { 220 | "text/plain": [ 221 | "[]" 222 | ] 223 | }, 224 | "metadata": { 225 | "tags": [] 226 | }, 227 | "execution_count": 25 228 | }, 229 | { 230 | "output_type": "display_data", 231 | "data": { 232 | "image/png": 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WJHcgPyT3hKImL/Mqc8Rtp1wvTotk3q2F/dofWf8FyFewZZk871DUS15ljmHXc6nCfTv7JXDWfwHyFeTIfdjRbpLt92sxjFvmiFNuSdPVUvZFP1GfZkyi1RHIWZDJPc8e7kEnjrjbj3sCKmPN9qz0Kg2ZpHdt3US9HchZkGWZPHu40yx7O8x2iupqyUOv0tDf/dGl+ujMJWWHBgQvyJF7nqPdrE4ccbcTp9wz7N2RilB2aQgYVUEm9zSLaQ2S1YkjyXb6Jci85xcA1FOQZZk8O0WyKpNktZ2sykQAwhLkyF3KrxyQ1cU/cbczqORS9BoxAOoh2OSep6xOHIO2E6fkUuduGgD5CbIsk0TRFzslEafkUudumjxV+ecKFCGTkbuZXSnpE5LGJH3K3W/LYrt5GzQyzqMLJck245RcuP3cyZhkBjJI7mY2JumTkt4k6XFJ3zKzfe7+3bTbztugkXHWCSJp0olbchnUTTNqib/oG5EAVZRFWeYySY+5+w/d/QVJX5B0TQbbzV2/kXEeXShxttldTnjuhWMaP8XWvD5JyaVzMmkuLcv14skk9BIFk8xANsm9IeknXd8/3n5sDTO73swWzGzh6NGjGew2vahJx42TE7kkiDh3cupOxk8/tyJZ61Z0w7R0jmqbZL+fKzAqCptQdffd7j7t7tMbNmwoard99ZuMTJIg4k7eDdpm1A0/fvW0U/Wj296iB3dckaisMKojWCaZgWySe1PS+V3fv7z9WOX1u9gpboJIUvoYtM2sk/GojmCrsNwxULYsumW+JekVZnahWkn9HZL+OIPtFqLXZGSce352JJm8G9TZEjWBeoqZ5habiZNTnsswVB1r2mDUpU7u7n7MzD4gaV6tVsjPuPvh1JGVZH1Hy6B7fsYZbcftWOmVjDsxDNOpQ5skMLoy6XN393sl3ZvFtsoWNRK/5e7DQ7UrJml/7Hz/wS8e1KqvvUHdsK18jGCB0TTyV6iuFzUSf/q5laHq6Ek7VmamGjruve88GvpEKIDskNzX6TfZ2CshD5q8G2aSdFQnQgFkh4XD1pndtkXb9xzo+VxUQu5X+hhmYa9RnggFkI3ajNyLWghqZqqhyYnxns8NM3IepueaVj4AadVi5F70QlA3X31xZiPnJB0ro7gODIB81CK5F70QVNYthHE6VljJEECWapHcy7iMfn1C7pSF8hpVs5IhgCzVouZedvdI3qsrzi02e066SrQ/AhhOLZJ72QtBDbO6YtwJ4M6JIwrtjwCGUYuyTBY18DSTlXHLQp19NJeWZZI6lyL1q5/3OnF00P4IYFi1SO5Susvo005WxulVX7+P9deYRtXP+5VdrnstSwcAGE4tyjJppb1pRZyyUL8ReEevRN6v7HLX/mbwd00CkI+RSO5pu23iXFQUZ1u9EnmvE0fHKNw1CUA+alOWSWOYJQDWG1QWitpHR1T9vLPNpEseAEA/IzFyL6Lbptc+Ore2HrR8wMxUQw0WCwOQoZEYuRdx04q0+2CxMABZMo9YOzxP09PTvrCwUPh+q461ZQD0Y2b73X06zmtHYuReF9w1CUBWRqLmDgCjhuQOAAEiuQNAgKi5F4gJUwBFIbkXhJtxACgSZZmCpF3fBgCSILkXpIy7SQEYXZRluuRZE89ifRsAiIuRe1vet9Ir+25SAEYLyb0t75p4nGWDASArlGXaiqiJs7wAgKIwcm+Lqn1TEwdQRyT3NmriAEJCWaatiDXfAaAoJPcu1MQBhIKyDAAEiOQOAAEiuQNAgEjuABAgkjsABChVcjezt5vZYTM7bmax7sgNAMhf2pH7I5KulfRABrEAADKSqs/d3R+VJDPLJhoAQCYKq7mb2fVmtmBmC0ePHi1qtwAwkgaO3M3s65Je1uOpD7n7l+PuyN13S9otSdPT0x47QgBAYgOTu7u/sYhAAADZoRUSAAKUthXybWb2uKTXSbrHzOazCQsAkEbabpkvSfpSRrEAADJS+yV/5xabrMEOAOvUOrnPLTa1c++hEze2bi4ta+feQ5JEggcw0mo9obpr/siJxN6xvLKqXfNHSooIAKqh1sn9iaXlRI8DwKiodXLfODmR6HEAGBW1Tu6z27ZoYnxszWMT42Oa3balpIgAoBpqPaHamTSlWwYA1qp1cpdaCZ5kDgBr1bosAwDojeQOAAEiuQNAgEjuABAgkjsABMjci78pkpn9UlId1gg4V9LPyg5iAGLMTh3irEOMUj3irEOM0to4L3D3DXH+UVmtkEfcfbqkfcdmZgtVj5MYs1OHOOsQo1SPOOsQozR8nJRlACBAJHcACFBZyX13SftNqg5xEmN26hBnHWKU6hFnHWKUhoyzlAlVAEC+KMsAQIBI7gAQoEKSu5m93cwOm9lxM4ts6TGzK83siJk9ZmY7ioht3f7PMbOvmdn323+fHfG6VTM70P6zr6DY+h4bMzvNzPa0n3/YzDYXEVfCGN9rZke7jt2flRDjZ8zsKTN7JOJ5M7O/b7+H75jZayoY4xvM7Jmu43hj0TG24zjfzO43s++2f7//qsdrSj2eMWMs/Xia2elm9k0zO9iO85Yer0n2O+7uuf+R9OuStkj6hqTpiNeMSfqBpIsk/Yqkg5JeVUR8XTH8raQd7a93SPpYxOueLTiugcdG0l9I+qf21++QtKeCMb5X0j8UGVePOH9H0mskPRLx/FWSvirJJG2V9HAFY3yDpK+UeRzbcZwn6TXtr39N0n/2+JmXejxjxlj68WwfnzPbX49LeljS1nWvSfQ7XsjI3d0fdfdBV6ReJukxd/+hu78g6QuSrsk/ujWukfTZ9teflTRT8P6jxDk23bHfKen3zMwqFmPp3P0BST/v85JrJH3OWx6SNGlm5xUTXUuMGCvB3Z9092+3v/6lpEclrb+5QqnHM2aMpWsfn2fb3463/6zvdkn0O16lmntD0k+6vn9cxf8QXuruT7a//m9JL4143elmtmBmD5lZESeAOMfmxGvc/ZikZyS9pIDYTtp/W9TP77r2x/M7zez8YkJLpAr/D+N4Xfsj/FfN7OKyg2mXCKbUGnF2q8zx7BOjVIHjaWZjZnZA0lOSvubukccyzu94ZssPmNnXJb2sx1MfcvcvZ7WftPrF2f2Nu7uZRfWJXuDuTTO7SNJ9ZnbI3X+QdawBulvS7e7+vJn9uVqjkCtKjqmOvq3W/8FnzewqSXOSXlFWMGZ2pqS7JG1391+UFUc/A2KsxPF091VJl5rZpKQvmdmr3b3nvEscmSV3d39jyk00JXWP5F7efixT/eI0s5+a2Xnu/mT7o+NTEdtotv/+oZl9Q63RQJ7JPc6x6bzmcTM7VdJZkv4nx5jWGxiju3fH8ym15jiqppD/h2l0Jyd3v9fM/tHMznX3whfBMrNxtZLm5919b4+XlH48B8VYpePZjmHJzO6XdKWk7uSe6He8SmWZb0l6hZldaGa/otaEQSGdKF32SXpP++v3SDrpE4eZnW1mp7W/PlfS5ZK+m3NccY5Nd+x/KOk+b8+8FGRgjOtqrVerVf+smn2S/rTd5bFV0jNdpbpKMLOXdWqtZnaZWr/HRZ7IO3GYpE9LetTdPx7xslKPZ5wYq3A8zWxDe8QuM5uQ9CZJ31v3smS/4wXNBL9NrVrb85J+Kmm+/fhGSfd2ve4qtWazf6BWOafoGeuXSPo3Sd+X9HVJ57Qfn5b0qfbXr5d0SK1ukEOS3ldQbCcdG0kfkXR1++vTJd0h6TFJ35R0UQnHb1CMt0o63D5290t6ZQkx3i7pSUkr7f+T75P0fknvbz9vkj7Zfg+HFNHdVXKMH+g6jg9Jen3RMbbj+G21Jv2+I+lA+89VVTqeMWMs/XhK+g1Ji+04H5F0Y/vxoX/HWX4AAAJUpbIMACAjJHcACBDJHQACRHIHgACR3AEgQCR3AAgQyR0AAvT/de5L8XElNq8AAAAASUVORK5CYII=\n", 233 | "text/plain": [ 234 | "
" 235 | ] 236 | }, 237 | "metadata": { 238 | "tags": [], 239 | "needs_background": "light" 240 | } 241 | } 242 | ] 243 | }, 244 | { 245 | "cell_type": "code", 246 | "metadata": { 247 | "id": "4eAoOR9SndVn", 248 | "colab_type": "code", 249 | "colab": { 250 | "base_uri": "https://localhost:8080/", 251 | "height": 283 252 | }, 253 | "outputId": "bfa8f7a6-cd13-4af9-cfa0-015f89fb4909" 254 | }, 255 | "source": [ 256 | "x = x - np.mean(x)\n", 257 | "y = y - np.mean(y)\n", 258 | "plt.plot(x, y, 'o')" 259 | ], 260 | "execution_count": 26, 261 | "outputs": [ 262 | { 263 | "output_type": "execute_result", 264 | "data": { 265 | "text/plain": [ 266 | "[]" 267 | ] 268 | }, 269 | "metadata": { 270 | "tags": [] 271 | }, 272 | "execution_count": 26 273 | }, 274 | { 275 | "output_type": "display_data", 276 | "data": { 277 | "image/png": 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\n", 278 | "text/plain": [ 279 | "
" 280 | ] 281 | }, 282 | "metadata": { 283 | "tags": [], 284 | "needs_background": "light" 285 | } 286 | } 287 | ] 288 | }, 289 | { 290 | "cell_type": "code", 291 | "metadata": { 292 | "id": "QneMf54BpAg0", 293 | "colab_type": "code", 294 | "colab": { 295 | "base_uri": "https://localhost:8080/", 296 | "height": 35 297 | }, 298 | "outputId": "0fb08a46-bdae-48b0-822b-3223ee00967d" 299 | }, 300 | "source": [ 301 | "b = sum(y * x) / sum(x ** 2 )\n", 302 | "b" 303 | ], 304 | "execution_count": 27, 305 | "outputs": [ 306 | { 307 | "output_type": "execute_result", 308 | "data": { 309 | "text/plain": [ 310 | "0.7831514763655998" 311 | ] 312 | }, 313 | "metadata": { 314 | "tags": [] 315 | }, 316 | "execution_count": 27 317 | } 318 | ] 319 | }, 320 | { 321 | "cell_type": "code", 322 | "metadata": { 323 | "id": "N88itcqLpM20", 324 | "colab_type": "code", 325 | "colab": { 326 | "base_uri": "https://localhost:8080/", 327 | "height": 283 328 | }, 329 | "outputId": "692e5d49-6eaf-45f7-920b-d0b91384b77b" 330 | }, 331 | "source": [ 332 | "plt.plot(x, y, 'o')\n", 333 | "t = np.array([-1.5, 2.5])\n", 334 | "plt.plot(t, t * b)" 335 | ], 336 | "execution_count": 28, 337 | "outputs": [ 338 | { 339 | "output_type": "execute_result", 340 | "data": { 341 | "text/plain": [ 342 | "[]" 343 | ] 344 | }, 345 | "metadata": { 346 | "tags": [] 347 | }, 348 | "execution_count": 28 349 | }, 350 | { 351 | "output_type": "display_data", 352 | "data": { 353 | "image/png": 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\n", 354 | "text/plain": [ 355 | "
" 356 | ] 357 | }, 358 | "metadata": { 359 | "tags": [], 360 | "needs_background": "light" 361 | } 362 | } 363 | ] 364 | } 365 | ] 366 | } -------------------------------------------------------------------------------- /notebooks/tensorflow_example.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "tensorflow example", 7 | "provenance": [], 8 | "authorship_tag": "ABX9TyM1QXcrvPV3uAYSwBe6bdaG", 9 | "include_colab_link": true 10 | }, 11 | "kernelspec": { 12 | "name": "python3", 13 | "display_name": "Python 3" 14 | } 15 | }, 16 | "cells": [ 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "id": "view-in-github", 21 | "colab_type": "text" 22 | }, 23 | "source": [ 24 | "\"Open" 25 | ] 26 | }, 27 | { 28 | "cell_type": "markdown", 29 | "metadata": { 30 | "id": "CPJWI12Vjsb2", 31 | "colab_type": "text" 32 | }, 33 | "source": [ 34 | "Illustrating TF in a colab notebook. Code taken from:\n", 35 | "[the TF team's colab notebook](https://colab.research.google.com/github/tensorflow/docs/blob/master/site/en/tutorials/quickstart/beginner.ipynb#scrollTo=rYb6DrEH0GMv)." 36 | ] 37 | }, 38 | { 39 | "cell_type": "code", 40 | "metadata": { 41 | "id": "IA6Tq3mCjq1h", 42 | "colab_type": "code", 43 | "colab": {} 44 | }, 45 | "source": [ 46 | "import tensorflow as tf\n", 47 | "import matplotlib.pyplot as plt\n", 48 | "import numpy as np\n" 49 | ], 50 | "execution_count": 0, 51 | "outputs": [] 52 | }, 53 | { 54 | "cell_type": "markdown", 55 | "metadata": { 56 | "id": "VK0xN0GvkBaH", 57 | "colab_type": "text" 58 | }, 59 | "source": [ 60 | "Import the data. It's a collection of 28x28 images of handwritten digits." 61 | ] 62 | }, 63 | { 64 | "cell_type": "code", 65 | "metadata": { 66 | "id": "v8IZXT5Bj_QR", 67 | "colab_type": "code", 68 | "colab": { 69 | "base_uri": "https://localhost:8080/", 70 | "height": 53 71 | }, 72 | "outputId": "fdbc1a69-e7cb-4341-b3af-afde774af2cb" 73 | }, 74 | "source": [ 75 | "mnist = tf.keras.datasets.mnist\n", 76 | "\n", 77 | "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", 78 | "x_train, x_test = x_train / 255.0, x_test / 255.0" 79 | ], 80 | "execution_count": 2, 81 | "outputs": [ 82 | { 83 | "output_type": "stream", 84 | "text": [ 85 | "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n", 86 | "11493376/11490434 [==============================] - 0s 0us/step\n" 87 | ], 88 | "name": "stdout" 89 | } 90 | ] 91 | }, 92 | { 93 | "cell_type": "code", 94 | "metadata": { 95 | "id": "5TqQCQbokIpy", 96 | "colab_type": "code", 97 | "colab": { 98 | "base_uri": "https://localhost:8080/", 99 | "height": 35 100 | }, 101 | "outputId": "5e62106d-762b-4d58-d0a5-fef098e338b2" 102 | }, 103 | "source": [ 104 | "[x_train.shape, y_train.shape, x_test.shape, y_test.shape]" 105 | ], 106 | "execution_count": 5, 107 | "outputs": [ 108 | { 109 | "output_type": "execute_result", 110 | "data": { 111 | "text/plain": [ 112 | "[(60000, 28, 28), (60000,), (10000, 28, 28), (10000,)]" 113 | ] 114 | }, 115 | "metadata": { 116 | "tags": [] 117 | }, 118 | "execution_count": 5 119 | } 120 | ] 121 | }, 122 | { 123 | "cell_type": "code", 124 | "metadata": { 125 | "id": "X35HH3abk2h6", 126 | "colab_type": "code", 127 | "colab": { 128 | "base_uri": "https://localhost:8080/", 129 | "height": 283 130 | }, 131 | "outputId": "729d9c68-425c-4ed9-9b8f-a12e57fc2c96" 132 | }, 133 | "source": [ 134 | "plt.imshow(x_train[2,:,:])" 135 | ], 136 | "execution_count": 11, 137 | "outputs": [ 138 | { 139 | "output_type": "execute_result", 140 | "data": { 141 | "text/plain": [ 142 | "" 143 | ] 144 | }, 145 | "metadata": { 146 | "tags": [] 147 | }, 148 | "execution_count": 11 149 | }, 150 | { 151 | "output_type": "display_data", 152 | "data": { 153 | "image/png": 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" 156 | ] 157 | }, 158 | "metadata": { 159 | "tags": [], 160 | "needs_background": "light" 161 | } 162 | } 163 | ] 164 | }, 165 | { 166 | "cell_type": "markdown", 167 | "metadata": { 168 | "id": "vCaMoLHQl0LW", 169 | "colab_type": "text" 170 | }, 171 | "source": [ 172 | "Create a model that has \n", 173 | "\n", 174 | "* The input layer flattened from 28x28 to a vector\n", 175 | "* A fully connected layer with 128 hidden nodes\n", 176 | "* A dropout layer with 20% dropout\n", 177 | "* A fully connected layer with 10 nodes\n", 178 | "\n", 179 | "Note the output layer is not included in the model." 180 | ] 181 | }, 182 | { 183 | "cell_type": "code", 184 | "metadata": { 185 | "id": "B-62W8c2lvNG", 186 | "colab_type": "code", 187 | "colab": {} 188 | }, 189 | "source": [ 190 | "model = tf.keras.models.Sequential([\n", 191 | " tf.keras.layers.Flatten(input_shape=(28, 28)),\n", 192 | " tf.keras.layers.Dense(128, activation='relu'),\n", 193 | " tf.keras.layers.Dropout(0.2),\n", 194 | " tf.keras.layers.Dense(10)\n", 195 | "])\n" 196 | ], 197 | "execution_count": 0, 198 | "outputs": [] 199 | }, 200 | { 201 | "cell_type": "code", 202 | "metadata": { 203 | "id": "f34z5x1am7f1", 204 | "colab_type": "code", 205 | "colab": { 206 | "base_uri": "https://localhost:8080/", 207 | "height": 307 208 | }, 209 | "outputId": "e097ae94-30b6-42b4-f391-4e20bd257409" 210 | }, 211 | "source": [ 212 | "model.summary()" 213 | ], 214 | "execution_count": 15, 215 | "outputs": [ 216 | { 217 | "output_type": "stream", 218 | "text": [ 219 | "Model: \"sequential\"\n", 220 | "_________________________________________________________________\n", 221 | "Layer (type) Output Shape Param # \n", 222 | "=================================================================\n", 223 | "flatten (Flatten) (None, 784) 0 \n", 224 | "_________________________________________________________________\n", 225 | "dense (Dense) (None, 128) 100480 \n", 226 | "_________________________________________________________________\n", 227 | "dropout (Dropout) (None, 128) 0 \n", 228 | "_________________________________________________________________\n", 229 | "dense_1 (Dense) (None, 10) 1290 \n", 230 | "=================================================================\n", 231 | "Total params: 101,770\n", 232 | "Trainable params: 101,770\n", 233 | "Non-trainable params: 0\n", 234 | "_________________________________________________________________\n" 235 | ], 236 | "name": "stdout" 237 | } 238 | ] 239 | }, 240 | { 241 | "cell_type": "markdown", 242 | "metadata": { 243 | "id": "Kd0oI31SmaKS", 244 | "colab_type": "text" 245 | }, 246 | "source": [ 247 | "Now that we've created the model, it gets initialized with weights. Of course, these aren't good weights. But, we can illustrate forward propagation through the network." 248 | ] 249 | }, 250 | { 251 | "cell_type": "code", 252 | "metadata": { 253 | "id": "9rjPWw1Lm1Ar", 254 | "colab_type": "code", 255 | "colab": { 256 | "base_uri": "https://localhost:8080/", 257 | "height": 71 258 | }, 259 | "outputId": "b47e4518-a12d-46e5-c818-10c555b972f7" 260 | }, 261 | "source": [ 262 | "model(x_test[:1]).numpy()" 263 | ], 264 | "execution_count": 16, 265 | "outputs": [ 266 | { 267 | "output_type": "execute_result", 268 | "data": { 269 | "text/plain": [ 270 | "array([[ 0.38137725, 0.3295499 , -0.03025779, 0.20247848, -0.11673211,\n", 271 | " -0.20458013, -0.10713655, -0.05961871, -0.08456571, 0.44097432]],\n", 272 | " dtype=float32)" 273 | ] 274 | }, 275 | "metadata": { 276 | "tags": [] 277 | }, 278 | "execution_count": 16 279 | } 280 | ] 281 | }, 282 | { 283 | "cell_type": "markdown", 284 | "metadata": { 285 | "id": "2DpoGZ4knK_o", 286 | "colab_type": "text" 287 | }, 288 | "source": [ 289 | "" 290 | ] 291 | } 292 | ] 293 | } -------------------------------------------------------------------------------- /old/labSyllabus.md: -------------------------------------------------------------------------------- 1 | This is the old syllabus, look at the teams site for the updated one 2 | 3 | # Lab syllabus 4 | 5 | 1. Introduction to Python 6 | 1. Installing python 7 | 2. Chosing an IDE 8 | 3. Jupyter notebooks 9 | 4. Importing libraries 10 | 5. Basic arthmetic 11 | 6. Basic data import 12 | 7. Basic markdown 13 | 8. Basic git and github 14 | 9. Project: Cloning a github repo, creating a jupyeter notebook, adding it to version control, reading in a dataset, performing a basic manipulation, commiting changes to git, pushing changes to github. 15 | 2. Tour of programming in python 16 | 1. Control flow 17 | 2. Data structures 18 | 3. Creating functions 19 | 4. OOP concepts in python 20 | 5. text processing 21 | 6. Project: write a basic prediction function using thresholding and MRIcloud values. 22 | 3. NumPy and matplotlib 23 | 1. Plotting in python 24 | 2. Arrays and mathematical data structures in python 25 | 3. Project: creating an 3D array of MRIcloud imaging data. Performing a simple statistical summary across one dimension of the array. Plotting the result. 26 | 4. Pandas 27 | 1. Data manipulation and cleaning 28 | 2. Project: reading in MRICloud text data; putting it into a pandas dataframe. Performing data wrangling on the datarfame. Creating numerical summaries and exploratory plots. 29 | 5. Pytorch, Scipy 30 | 1. Regression, linear and generalized linear models in python 31 | 2. Setting up pytorch 32 | 3. Pip and conda. 33 | 4. Project: prediction Alzheimer's disease status using the ADNI database. 34 | 6. Lab on running deep networks in python 35 | 1. Project: convoluational neural network for lesion segmentation. 36 | 7. Lab on running deep networks and evaluation 37 | 1. Project: evaluation of a NN algorithm for "Early Prediction of the Impending Onset of Septic Shock in Patients with Sepsis." 38 | 39 | 40 | 41 | -------------------------------------------------------------------------------- /old/syllabus.md: -------------------------------------------------------------------------------- 1 | This is the old syllabus, look in the Teams site for the up to date syllabus 2 | 3 | # Introduction to data science syllabus 4 | 5 | * Instructors: Brian Caffo, Rai Winslow 6 | * Meeting time: Monday / Wednesday 3:00PM - 4:15PM (see below) 7 | * Office hours 8 | * TA office hours Friday 11:00AM - 11:50AM (see 9 | * Instructor office hours given over slack 10 | * Labs 11 | * Class location : online, asyncrhonous 12 | 13 | Books: 14 | 15 | * [Regression Models](https://leanpub.com/regmods) 16 | * [Goodfellow, Benjio and Courville, Deep Learning](https://www.deeplearningbook.org/) 17 | 18 | # Projects 19 | The projects are in an ipython notebook [here](https://colab.research.google.com/drive/1uHsNQUcCzsGSjbNy2ypf1XqGceDzyFIN?usp=sharing) 20 | 21 | # Grading 22 | 23 | Weekly projects counted equally. 24 | 25 | ## Lab course 26 | 27 | The associated lab course is mandatory. 28 | 29 | ## Colab ipython notebooks 30 | 31 | * [Notebook 1, some basic python and data input and munging](https://colab.research.google.com/drive/1oswpzvkRaphIkoTqXqa244kUWBSJfDw5) 32 | * [Notebook 2, simple classification and evaluation](https://colab.research.google.com/drive/1JzktE6vya812O6lbCy7rzrrt1YCAdIfE) 33 | * [Notebook 3, regression prediction](https://colab.research.google.com/drive/1rWDI6uNhLtwN8KPMPt5mhYaPqDixzWbQ) 34 | * [Notebook 4, regression classification](https://colab.research.google.com/drive/1Yc04O2KNHJ5GBFYE2Krt8cwJeNHwfOMb) 35 | 36 | ## Hand written notes 37 | 38 | I'll put a link to handwritten notes from the lectures here 39 | 40 | ## Class delivery 41 | This class will be delivered via recorded lectures. Instructor office 42 | hours will be held during a subset of course times, as well as others 43 | to accomodate foreign students in different time zones. Course 44 | communication will be held over slack. Invites to the slack group will 45 | be sent over email. 46 | 47 | * Recorded lectures (links will be posted here as well as the slack website) 48 | * Slack discussions 49 | * Live instructor office hours 50 | * Live TA office hours 51 | * Weekly projects to be handed in over github classroom 52 | * This github course site 53 | 54 | ## Lectures 55 | 56 | ## Class intstruction schedule and due dates 57 | 58 | ``` 59 | * Date , Instr, Due 60 | * 8/31 , Brian, 61 | * 9/2 , Brian, 62 | * 9/7 , Off , 63 | * 9/9 , Brian, Project 1 (note delayed due date) 64 | * 9/14 , Brian, Project 2 65 | * 9/16 , Brian, 66 | * 9/21 , Brian, Project 3 67 | * 9/23 , Brian, 68 | * 9/28 , Brian, Project 4 69 | * 9/30 , Brian, 70 | * 10/5 , Rai , Project 5 71 | * 10/7 , Rai , 72 | * 10/12, Rai , 73 | * 10/14, Rai , Project 6 74 | * 10/19, Rai , 75 | * 10/21, Rai , Project 7 76 | ``` 77 | 78 | ## Software / websites 79 | * [Google colab](https://colab.research.google.com/notebooks/intro.ipynb) we'll use colab to demonstrate some basics 80 | * [Azure notebooks](https://notebooks.azure.com/) we'll use this to demonstrate ipython notebooks 81 | * [Anaconda](https://www.anaconda.com/) For installing python, spyder and ipython notebooks locally 82 | * [git](https://git-scm.com/) Comes with most unix-like systems pre installed. If using Windows, install git 83 | * [github](www.github.com) 84 | 85 | 86 | ## Topics 87 | 0. Introduction to data science for BME 88 | 1. Git, Github 89 | 0. Google Colab 90 | 2. [Markdown](https://www.markdownguide.org/basic-syntax/) 91 | 3. Exploratory data analysis 92 | 4. [Reproducible research, replication crisis, some relevant links](https://github.com/bcaffo/ds4bme/blob/master/reproducible.md) 93 | 5. Computational topics: python and frameworks. 94 | 6. Example: reading in some MRI Cloud data 95 | 7. Grading and course structure; github classroom. 96 | 1. Introduction to classification and prediction 97 | 1. Classification with one continuous predictor and thresholding 98 | 2. Simple regression prediction through the origin 99 | 3. Loss functions, squared error, cross entropy 100 | 4. Example with voxel data 101 | 5. Computational topics, loading a simple dataset into a python notebook and creating a simple prediction algorithm 102 | 2. Linear separable models 103 | 1. Least squares prediction in a linear model 104 | 2. Binary least squares prediction with cross entropy error. 105 | 3. Example 106 | 4. Computational topics, building a linear model in python 107 | 3. Simple neural networks 108 | 1. Correspondence between network diagrams and loss functions 109 | 2. Example: fitting XOR with a neural network 110 | 3. Example: linear regression as a one layer 111 | 4. Example: binary logistic regression as a one layer NN 112 | 5. Example with MRI cloud data 113 | 6. Computational topics: installing pytorch (or TF?), pip or conda, ... 114 | 4. Deep neural networks 115 | 1. Fitting and back propagation 116 | 2. Dropout and regularization; bagging 117 | 3. Modern computational issues, GPU computing 118 | 4. Frameworks (TF, pytorch, ...) 119 | 5. Example: handwritten digit classification 120 | 6. Example: siamese network prediction using a deep neural network. 121 | 5. Special networks 122 | 1. Convoluational NNs. 123 | 2. Recurrent NNs. 124 | 3. Autoencoders. 125 | 4. Example: cats versus dogs 126 | 5. Example: hand written digits 127 | 6. Example: activity classification ? 128 | 6. Evaluation 129 | 1. Overfitting 130 | 2. Evaluation metrics 131 | 3. Generalizability 132 | 4. Missing data 133 | 134 | -------------------------------------------------------------------------------- /old/test: -------------------------------------------------------------------------------- 1 | 2 | -------------------------------------------------------------------------------- /presentations/lecture1.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | DS4BME 2021 Lecture 1 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 25 | 26 | 27 |
28 |
29 |

DS4BME 2021 Lecture 1

Brian Caffo

Created: 2021-09-01 Wed 11:04

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Table of Contents

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1 Welcome

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1.1 Instructors

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1.1.1 Main class

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  • Brian Caffo
    • 73 |
  • Joseph Greenstein
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1.1.2 Lab

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  • Kwame Kutten
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2 Important

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90 | Get on the Teams site: 91 |

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  • Most important information will be given out over the General channel
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  • TA and Instructor office hours will be done on teams 95 |
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    • Go to the Office Hour channel and click on the video link
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    • 99 |
  • Main lectures given over zoom. Zoom link for Brian’s lectures will be the same 100 |
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    • Under General then Files you will find the course materials
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3 TAs

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  • We’re still adding TAs and have not met yet, so we’ll introduce all of the TAs at the next meeting
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117 | TAs will assist with grading and run the Friday office hours 118 |

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4 Software to install / try

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  • Google colab (cloud)
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  • Repl.it (cloud)
    • 128 |
  • Anaconda (local)
    • 129 |
  • Git (local)
    • 130 |
  • Github (cloud)
    • 131 |
  • Github desktop software (local)
    • 132 |
  • VS code (local)
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5 Projects

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  • Equally weighted projects, one per week
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  • Submitted via github classroom
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  • Note difference between github and github classroom
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  • Projects due Mondays at 5, unless Monday is a holiday then it wil be Tuesday at 5
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  • First project being written, it will only take a few minutes
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6 Grading

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  • Equally weighted projects
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  • Standard grading cutoffs
    • 158 |
  • Plus grades given for exceptional performance
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7 Syllabus / curriculum

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  • Under the channel General, then Files, then Class Materials
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  • Reminder to go through the syllabus
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8 Software

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  • Start to cover git, github, github classroom
    • 180 |
  • Markdown
    • 181 |
  • Google colab
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9 Code of conduct in the class

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  • Be nice!
    • 192 |
  • Be charitable about mistakes …
    • 193 |
  • Questions to the Teams site
    • 194 |
  • Instructor / TA communication to the Teams site (via chat)
    • 195 |
  • Do you own work, but feel free to ask questions, public on the Teams site better
    • 196 |
  • Everything that happens on Teams, stays on Teams (don't repost elsewhere)
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203 | 204 | 205 | 206 | 207 | 208 | 209 | 229 | 230 | 231 | -------------------------------------------------------------------------------- /presentations/lecture1.org: -------------------------------------------------------------------------------- 1 | #+Title: DS4BME 2021 Lecture 1 2 | #+Author: Brian Caffo 3 | #+EPRESENT_FRAME_LEVEL: 1 4 | 5 | * Welcome 6 | ** Instructors 7 | *** Main class 8 | - Brian Caffo 9 | - Joseph Greenstein 10 | *** Lab 11 | - Kwame Kutten 12 | 13 | * Important 14 | Get on the Teams site: 15 | - Most important information will be given out over the General channel 16 | - TA and Instructor office hours will be done on teams 17 | - Go to the Office Hour channel and click on the video link 18 | - Main lectures given over zoom. Zoom link for Brian’s lectures will be the same 19 | - Under General then Files you will find the course materials 20 | 21 | * TAs 22 | - We’re still adding TAs and have not met yet, so we’ll introduce all of the TAs at the next meeting 23 | TAs will assist with grading and run the Friday office hours 24 | 25 | * Software to install / try 26 | - Google colab (cloud) 27 | - Repl.it (cloud) 28 | - Anaconda (local) 29 | - Git (local) 30 | - Github (cloud) 31 | - Github desktop software (local) 32 | - VS code (local) 33 | 34 | * Projects 35 | - Equally weighted projects, one per week 36 | - Submitted via github classroom 37 | - Note difference between github and github classroom 38 | - Projects due Mondays at 5, unless Monday is a holiday then it wil be Tuesday at 5 39 | - First project being written, it will only take a few minutes 40 | 41 | * Grading 42 | - Equally weighted projects 43 | - Standard grading cutoffs 44 | - Plus grades given for exceptional performance 45 | 46 | * Syllabus / curriculum 47 | - Under the channel General, then Files, then Class Materials 48 | - Reminder to go through the syllabus 49 | 50 | * Software 51 | - Start to cover git, github, github classroom 52 | - Markdown 53 | - Google colab 54 | 55 | * Code of conduct in the class 56 | - Be nice! 57 | - Be charitable about mistakes ... 58 | - Questions to the Teams site 59 | - Instructor / TA communication to the Teams site (via chat) 60 | - Do you own work, but feel free to ask questions, public on the Teams site better 61 | - Everything that happens on Teams, stays on Teams (don't repost elsewhere) 62 | -------------------------------------------------------------------------------- /presentations/lecture2.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | DS4BME 2021 Lecture 2 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 25 | 26 | 27 |
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DS4BME 2021 Lecture 2

Brian Caffo

Created: 2021-09-01 Wed 13:33

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1 Reminders

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  • Get on the teams site!
    • 55 |
  • First project posted
    • 56 |
  • Take the quiz with your name and github username
    • 57 |
  • Watch the first video if you missed the first class
    • 58 | 59 |
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2 First project

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  • Reminder to go through the first project
    • 68 |
  • Due a week from Thursday
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  • No class on Monday
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3 TA sessions and office hour

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  • 11 - 12 to 1 - 4 on Fridays
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  • Go to the Office hours teams channel and click video link
    • 81 |
  • Instructor office hour 12 - 1 on Friday
    • 82 |
  • Also, by appointment
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4 TAs

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  • Chunming Gu (Lead TA)
    • 93 |
  • Yuta Kobayashi
    • 94 |
  • Marc Di Meo
    • 95 |
  • Dennis Gong
    • 96 |
  • Cassandra Parent
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5 TAs lab session

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  • Kalen Clifton (Lead TA)
    • 107 |
  • Ranjani Ramasubramanian
    • 108 |
  • Kevin Rao
    • 109 |
  • Yuan Zhou
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6 Thank you to the graders

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  • Samantha Weed
    • 120 |
  • Selena Kim
    • 121 |
  • Samantha “Sam” Tam
    • 122 |
  • Sundari Parise
    • 123 |
  • David Wang
    • 124 |
  • Min Joo
    • 125 |
  • Lily Zhu
    • 126 |
  • Ryan Zhao
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7 Notes I'm following

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8 Things to cover on github

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  • Your worst enemy
    • 149 |
  • Version control
    • 150 |
  • Github basics
    • 151 |
  • Differences with github classroom
    • 152 | 153 |
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9 Steps to cover

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  • Creating a repository
    • 162 |
  • Cloning a repository
    • 163 |
  • Forking a repository
    • 164 |
  • Adding files
    • 165 |
  • Deleting/moving/renaming files
    • 166 |
  • GH pages
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10 Getting started with programming with data

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  • Reading in data
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183 | 184 | 185 | 186 | 187 | 188 | 189 | 205 | 206 | 207 | -------------------------------------------------------------------------------- /presentations/lecture2.org: -------------------------------------------------------------------------------- 1 | #+Title: DS4BME 2021 Lecture 2 2 | #+Author: Brian Caffo 3 | #+EPRESENT_FRAME_LEVEL: 1 4 | 5 | * Reminders 6 | + Get on the teams site! 7 | + First project posted 8 | + Take the quiz with your name and github *username* 9 | + Watch the first video if you missed the first class 10 | 11 | * First project 12 | + Reminder to go through the first project 13 | + Due a week from Thursday 14 | + No class on Monday 15 | 16 | * TA sessions and office hour 17 | + 11 - 12 to 1 - 4 on Fridays 18 | + Go to the Office hours teams channel and click video link 19 | + Instructor office hour 12 - 1 on Friday 20 | + Also, by appointment 21 | 22 | * TAs 23 | + Chunming Gu (Lead TA) 24 | + Yuta Kobayashi 25 | + Marc Di Meo 26 | + Dennis Gong 27 | + Cassandra Parent 28 | 29 | * TAs lab session 30 | + Kalen Clifton (Lead TA) 31 | + Ranjani Ramasubramanian 32 | + Kevin Rao 33 | + Yuan Zhou 34 | 35 | * Thank you to the graders 36 | + Samantha Weed 37 | + Selena Kim 38 | + Samantha “Sam” Tam 39 | + Sundari Parise 40 | + David Wang 41 | + Min Joo 42 | + Lily Zhu 43 | + Ryan Zhao 44 | 45 | * Notes I'm following 46 | + [[https://bcaffo.github.io/ds4bio_book/_build/html/05-functions.html][Book]] 47 | + [[https://github.com/bcaffo/ds4bio_book][github repo for the book]] 48 | + [[https://github.com/bcaffo/ds4bme_intro][Course github site]] 49 | 50 | * Things to cover on github 51 | + Your worst enemy 52 | + Version control 53 | + Github basics 54 | + Differences with github classroom 55 | 56 | * Steps to cover 57 | + Creating a repository 58 | + Cloning a repository 59 | + Forking a repository 60 | + Adding files 61 | + Deleting/moving/renaming files 62 | + GH pages 63 | 64 | * Getting started with programming with data 65 | + Reading in data 66 | --------------------------------------------------------------------------------