logistic_regression_with_numpy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making the datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.random.multivariate_normal([1, 1], [[6, 0.5], [0.5, 4]], 500)\n",
    "x2 = np.random.multivariate_normal([-10, -1], [[4, 0.2], [0.2, 6]], 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fa8dd9325d0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2A3DMCKGCbthGEbEMGE3DMOIGP8PhFEx4AI6MwwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8dd9a2f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1[:, 0], x1[:, 1], c='blue', alpha = 0.3)\n",
    "plt.scatter(x2[:, 0], x2[:, 1], c='red', alpha = 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1 = np.array([0]* 500)\n",
    "y2 = np.array([1]* 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reshaping the input datasets into correct format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essentially we want to convert the predictor variable matrix into a nx by m dimensional matrix; and the target variable vector into a 1 by m dimensional matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictor shape:  (500, 2)\n",
      "target shape:  (500,)\n",
      "predictor shape:  (2, 500)\n",
      "target shape:  (1, 500)\n"
     ]
    }
   ],
   "source": [
    "print \"predictor shape: \", x1.shape\n",
    "print \"target shape: \", y1.shape\n",
    "\n",
    "x1 = x1.T\n",
    "y1 = y1.reshape(1, 500)\n",
    "\n",
    "x2 = x2.T\n",
    "y2 = y2.reshape(1, 500)\n",
    "\n",
    "print \"predictor shape: \", x1.shape\n",
    "print \"target shape: \", y1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stacking all the observed variables together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictor shape:  (2, 1000)\n",
      "target shape:  (1, 1000)\n"
     ]
    }
   ],
   "source": [
    "x = np.hstack((x1, x2))\n",
    "y = np.hstack((y1, y2))\n",
    "\n",
    "print \"predictor shape: \", x.shape\n",
    "print \"target shape: \", y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Making the train test split\n",
    "We will pick 0.7 * num_obs number of training examples at random and that will be out training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[476 589 625 304 397 103 164 402 870 670  87 554 626  75 501 592 469 426\n",
      " 983 106 583 243 841 148 221 929 282 638 455 800 986 295 572 960 348 712\n",
      " 542 703 331 255 848 939 130 704 878 915 341 463 279 710 447 313 732 802\n",
      "  49 183 143 872   1 598 614 984 942 122 827 799 522 679 709 497 319 283\n",
      "  34 578 997 671 765 186 150 214 806  51 597 956 559 157 239 209  36  61\n",
      " 432 346 557 492 509 567 374 624 284 736 952 486 574 971 160 869 271 526\n",
      " 936 226 362 990 126 490 613 445 278 191 190 706 216 782 673 149 603 151\n",
      " 678 897 657 393   0 415  17 442 117 411 927 735  94 210 639 441 561 770\n",
      " 940 444 979 840 311 739 296 185 364 562 240 246 788 382 292 101 987 508\n",
      " 349 380 429 795 171 803 734 496 819 651  92 551 258 410 876  80 810 746\n",
      " 705 968 980 124 787 933 175  70 177 966 527 301 546 730 317 176 287 324\n",
      " 361  14  40 756 577 981 431 198 403 325 888 145 552 208  12 204 964 834\n",
      "  55 761 751  24 694 889 749 360 234  50 443 850 345 154 104 913 982 801\n",
      " 967 949 245 464 581 701  66 826 137 996  20 928 973 436 392 312 440 169\n",
      " 918 959 686  98 351 854 909 767 528 193 286 147 268  23 471  44  97 821\n",
      " 451 159 368 555 606 727 507 181 182 141 153 728 605 565 144 556 857 251\n",
      " 825 424 633 300 937 257 866 213  60 343 276 760 762 125 237 232 413 851\n",
      " 721 435 741 227 934 249 207 503 330 222 494  62  79 323 288 951 376 519\n",
      " 923 355 617 306 745 414 953 569 264 510 110 912 903  45 784 493 864 158\n",
      "  26 238  72  41 405 353  18 861 684 161 344  82 192 965 538 610 422 366\n",
      " 127 450 231 865 585 548 677 649 668 115 299 875 454  84 167 829 498 682\n",
      " 135 957 794 118 340 902 434 102 489 199 919 907  35 381 886 457 259 958\n",
      " 462 899 683 662 395 972  95 163 474 518 742 962 750 999 525 707 529 423\n",
      " 618 849 674 858  31 579 335 200 924 217 895  39 804 860 534 724 648 314\n",
      " 128 479 570 517 456 659 220 807 660  58 797 544 873 512  22 320 499 107\n",
      " 900 468 187  64 485 715 623 693  57 944 326 223 954 887 384 780 256 573\n",
      " 506 196 298  15 437 631 387 883 394 294 385 824 390 629 448 666 992 484\n",
      " 586 113 459 917 121 558 533 720 880 717 595  63 893 652 754 400 738 513\n",
      " 180 882 692 203 748 600 262 134 377 778 224 867 371 884   9 229 947 828\n",
      " 591 347 515 303  74 244 236 743 759 758 100 695 619 616 105 205  13 969\n",
      " 142 699 687 847 263 502 601 596 853 863 520 792 535 321 427 622 575  56\n",
      " 691 920 242 566 843 375 481 123 452 273 419 916 230 978 609 478 700 711\n",
      " 943 839 315 266 131 955 768 628 536 676 252 961 874  68 771  29 718 545\n",
      " 708 832 417 162 539 811 988 644 635 630 932 383 868  16 667 297 830 537\n",
      " 755 318  48 218 922 465  76 898 789 540 643 891 308 813 407 178 119 612\n",
      " 582 399  21 172 305 963  47 428  37 744 250  67 831 991 653 791 108 487\n",
      " 785 524 560 491 514 401 798 280 615 248 293   3 170 418  19 156 370  93\n",
      " 647 846  77 379 753 908 247 790  53 719 911   6 680 195 910 549 453 993\n",
      " 367 580 564 116 467 378 685 543 281 833 328  42 470 261 339 881]\n",
      "[  2   4   5   7   8  10  11  25  27  28  30  32  33  38  43  46  52  54\n",
      "  59  65  69  71  73  78  81  83  85  86  88  89  90  91  96  99 109 111\n",
      " 112 114 120 129 132 133 136 138 139 140 146 152 155 165 166 168 173 174\n",
      " 179 184 188 189 194 197 201 202 206 211 212 215 219 225 228 233 235 241\n",
      " 253 254 260 265 267 269 270 272 274 275 277 285 289 290 291 302 307 309\n",
      " 310 316 322 327 329 332 333 334 336 337 338 342 350 352 354 356 357 358\n",
      " 359 363 365 369 372 373 386 388 389 391 396 398 404 406 408 409 412 416\n",
      " 420 421 425 430 433 438 439 446 449 458 460 461 466 472 473 475 477 480\n",
      " 482 483 488 495 500 504 505 511 516 521 523 530 531 532 541 547 550 553\n",
      " 563 568 571 576 584 587 588 590 593 594 599 602 604 607 608 611 620 621\n",
      " 627 632 634 636 637 640 641 642 645 646 650 654 655 656 658 661 663 664\n",
      " 665 669 672 675 681 688 689 690 696 697 698 702 713 714 716 722 723 725\n",
      " 726 729 731 733 737 740 747 752 757 763 764 766 769 772 773 774 775 776\n",
      " 777 779 781 783 786 793 796 805 808 809 812 814 815 816 817 818 820 822\n",
      " 823 835 836 837 838 842 844 845 852 855 856 859 862 871 877 879 885 890\n",
      " 892 894 896 901 904 905 906 914 921 925 926 930 931 935 938 941 945 946\n",
      " 948 950 970 974 975 976 977 985 989 994 995 998]\n"
     ]
    }
   ],
   "source": [
    "trn = np.random.choice(x.shape[1], int(0.7 * x.shape[1]), replace = False)\n",
    "print trn\n",
    "\n",
    "tst = np.setdiff1d(np.array(range(x.shape[1])), trn)\n",
    "print tst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x[:, trn]\n",
    "y_train = y[:, trn]\n",
    "\n",
    "x_test = x[:, tst]\n",
    "y_test = y[:, tst]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 700)\n",
      "(1, 700)\n",
      "(2, 300)\n",
      "(1, 300)\n"
     ]
    }
   ],
   "source": [
    "print x_train.shape\n",
    "print y_train.shape\n",
    "\n",
    "print x_test.shape\n",
    "print y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ready for the real deal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Sigmoid Function\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1/(1 + np.exp(-x))\n",
    "\n",
    "\n",
    "# initialize the parameters\n",
    "\n",
    "def initialize_with_zeros(dim):\n",
    "    w = np.zeros((dim, 1))\n",
    "    b = 0.0\n",
    "    return w, b\n",
    "\n",
    "# propagation\n",
    "\n",
    "def prop(w, b, x, y):\n",
    "    m = x.shape[1]\n",
    "    \n",
    "    A = sigmoid(np.add(np.dot(w.T, x), b))    \n",
    "    cost = (-1. / m) * np.sum(y * np.log(A) + (1 - y) * np.log(1 - A))\n",
    "\n",
    "    dw = 1. / m * np.sum(np.dot(x, (A - y).T))\n",
    "    db = 1. / m * np.sum(A - y)\n",
    "    \n",
    "    grads = {\"dw\": dw, \"db\": db}\n",
    "\n",
    "    return grads, cost\n",
    "\n",
    "# optimize\n",
    "\n",
    "def optimize(w, b, x, y, num_iterations, learning_rate):\n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        grad, cost = prop(w, b, x, y)\n",
    "        dw = grad[\"dw\"]\n",
    "        db = grad[\"db\"]\n",
    "        \n",
    "        w = w - learning_rate * grad[\"dw\"]\n",
    "        b = b - learning_rate * grad[\"db\"]\n",
    "        \n",
    "        if i % (num_iterations / 10) == 0:\n",
    "            costs.append(cost)\n",
    "            print \"Cost after \", i, \" iterations: \", cost\n",
    "    print \"Cost after \", num_iterations, \" iterations: \", cost\n",
    "    params = {\"w\": w, \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw, \"db\": db}\n",
    "    \n",
    "    return params, grads, costs\n",
    "\n",
    "\n",
    "# predict\n",
    "\n",
    "def predict(w, b, x):\n",
    "    m = x.shape[1]\n",
    "    \n",
    "#    y_pred = np.zeros((1, m))\n",
    "    y_pred = sigmoid(np.add(np.dot(w.T, x), b))[0]\n",
    "    \n",
    "#     print y_pred\n",
    "    \n",
    "    y_predictions = np.array(map(lambda i: 1 if i > 0.5 else 0, y_pred))\n",
    "    y_predictions = y_predictions.reshape(1, m)\n",
    "    \n",
    "#     print y_predictions\n",
    "    \n",
    "    return y_predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Actual Model built with all the helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# model\n",
    "\n",
    "def model(x_train, y_train, x_test, y_test, learning_rate, num_iterations):\n",
    "    dim = x_train.shape[0]\n",
    "    \n",
    "    w, b = initialize_with_zeros(dim)\n",
    "    \n",
    "    params, grads, costs = optimize(w, b, x_train, y_train, num_iterations, learning_rate)\n",
    "    \n",
    "    w = params[\"w\"]\n",
    "    b = params[\"b\"]\n",
    "    \n",
    "    y_pred_train = predict(w, b, x_train)\n",
    "    y_pred_test = predict(w, b, x_test)\n",
    "    \n",
    "    print \"Training Accuracy: \", (1. - np.mean(np.abs(y_train - y_pred_train))) * 100., \" percent\"\n",
    "    print \"Test Accuracy: \", (1. - np.mean(np.abs(y_test - y_pred_test))) * 100., \" percent\"\n",
    "    \n",
    "    model_char = {\"w\": w, \"b\": b, \"costs\": costs, \"learning_rate\": learning_rate, \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return model_char\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after  0  iterations:  0.69314718056\n",
      "Cost after  1000  iterations:  0.164197986651\n",
      "Cost after  2000  iterations:  0.127740802882\n",
      "Cost after  3000  iterations:  0.111539875136\n",
      "Cost after  4000  iterations:  0.102398657746\n",
      "Cost after  5000  iterations:  0.0965239898771\n",
      "Cost after  6000  iterations:  0.0924306127042\n",
      "Cost after  7000  iterations:  0.0894176196947\n",
      "Cost after  8000  iterations:  0.0871104363436\n",
      "Cost after  9000  iterations:  0.0852902970896\n",
      "Cost after  10000  iterations:  0.0838219686675\n",
      "Training Accuracy:  97.0  percent\n",
      "Test Accuracy:  98.0  percent\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'b': -3.4221866029282091,\n",
       " 'costs': [0.6931471805599454,\n",
       "  0.16419798665062593,\n",
       "  0.12774080288222914,\n",
       "  0.11153987513626662,\n",
       "  0.10239865774553623,\n",
       "  0.096523989877148789,\n",
       "  0.09243061270417359,\n",
       "  0.089417619694654601,\n",
       "  0.087110436343636133,\n",
       "  0.085290297089594319],\n",
       " 'learning_rate': 0.01,\n",
       " 'num_iterations': 10000,\n",
       " 'w': array([[-0.80808911],\n",
       "        [-0.80808911]])}"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(x_train, y_train, x_test, y_test, learning_rate= 0.01, num_iterations=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}