CS 156a Set 6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "train = np.loadtxt(fname = \"C:\\\\Users\\\\Spencer\\\\Downloads\\\\in.dta.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.loadtxt(fname = \"C:\\\\Users\\\\Spencer\\\\Downloads\\\\out.dta.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlinear_transformation_regression(training_pts, labels):\n",
    "    missclassified = 0\n",
    "    transformed_pts = np.asarray(nonlinear_transform(training_pts))\n",
    "    pseudo_inverse = np.linalg.pinv(transformed_pts)\n",
    "    y = np.asarray(labels)\n",
    "    w = np.matmul(pseudo_inverse, y)\n",
    "    for i in range(len(pts)):\n",
    "        if np.sign(w.dot(transformed_pts[i])) != labels[i]:\n",
    "            missclassified += 1\n",
    "    return (w, missclassified / len(pts)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regression_with_decay(training_pts, labels, k):\n",
    "    missclassified = 0\n",
    "    transformed_pts = np.asarray(nonlinear_transform(training_pts))\n",
    "    pseudo_inverse = np.linalg.pinv(transformed_pts)\n",
    "    y = np.asarray(labels)\n",
    "    col = transformed_pts.shape[1]\n",
    "    inner_term = np.linalg.inv((np.matmul(transformed_pts.T, transformed_pts) + 10**k * np.identity(col)))\n",
    "    x = np.matmul(transformed_pts.T, transformed_pts)\n",
    "    intermed = np.matmul(inner_term, transformed_pts.T)\n",
    "    w = np.matmul(intermed, y)\n",
    "    for i in range(len(pts)):\n",
    "        if np.sign(w.dot(transformed_pts[i])) != labels[i]:\n",
    "            missclassified += 1\n",
    "    return (w, missclassified / len(pts)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlinear_transform(pts):\n",
    "    transformation = []\n",
    "    for pt in pts:\n",
    "        x1 = pt[0]\n",
    "        x2 = pt[1]\n",
    "        transformation.append([1, x1, x2, x1 ** 2, x2 ** 2, x1 * x2, abs((x1 - x2)), abs((x1 + x2))])\n",
    "    return transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = []\n",
    "for i in range(len(train)):\n",
    "    y.append(train[i][2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = []\n",
    "for i in range(len(train)):\n",
    "    pts.append((train[i][0], train[i][1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "out_labels = []\n",
    "for i in range(len(test)):\n",
    "    out_labels.append(test[i][2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_pts = []\n",
    "for i in range(len(test)):\n",
    "    test_pts.append((test[i][0], test[i][1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.02857142857142857,\n",
       " array([-1.64706706, -0.14505927,  0.10154121, -2.03296844, -1.82804373,\n",
       "         2.48152945,  4.15893861,  0.31651714]))"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_in = 0\n",
    "w = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = nonlinear_transformation_regression(pts, y)\n",
    "e_in += x[1]\n",
    "w += x[0]\n",
    "(e_in, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.084"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_out = 0\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out = missclassified / len(test_pts)\n",
    "e_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.02857142857142857,\n",
       " array([-1.6432827 , -0.14333537,  0.10144329, -2.02456533, -1.81721505,\n",
       "         2.45550685,  4.14009201,  0.31960135]))"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_in_decay_small = 0\n",
    "w_decay_small = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, -3)\n",
    "e_in_decay_small += x[1]\n",
    "w_decay_small += x[0]\n",
    "(e_in_decay_small, w_decay_small)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_small.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_small = missclassified / len(test_pts)\n",
    "e_out_decay_small"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.37142857142857144,\n",
       " array([ 0.00435688, -0.00134416,  0.0024939 ,  0.00328695,  0.00484127,\n",
       "        -0.00862023,  0.01786706, -0.00490192]))"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_in_decay_big = 0\n",
    "w_decay_big = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, 3)\n",
    "e_in_decay_big += x[1]\n",
    "w_decay_big += x[0]\n",
    "(e_in_decay_big, w_decay_big)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.436"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_big.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_big = missclassified / len(test_pts)\n",
    "e_out_decay_big"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.228, 0.124, 0.092, 0.056, 0.084)"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_decay_2 = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, 2)\n",
    "w_decay_2 += x[0]\n",
    "(w_decay_2)\n",
    "\n",
    "w_decay_1 = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, 1)\n",
    "w_decay_1 += x[0]\n",
    "(w_decay_1)\n",
    "\n",
    "w_decay_0 = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, 0)\n",
    "w_decay_0 += x[0]\n",
    "(w_decay_0)\n",
    "\n",
    "w_decay_neg1 = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, -1)\n",
    "w_decay_neg1 += x[0]\n",
    "(w_decay_neg1)\n",
    "\n",
    "w_decay_neg2 = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "x = regression_with_decay(pts, y, -2)\n",
    "w_decay_neg2 += x[0]\n",
    "(w_decay_neg2)\n",
    "\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_2.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_2 = missclassified / len(test_pts)\n",
    "\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_1.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_1 = missclassified / len(test_pts)\n",
    "\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_0.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_0 = missclassified / len(test_pts)\n",
    "\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_neg1.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_neg1 = missclassified / len(test_pts)\n",
    "\n",
    "missclassified = 0\n",
    "transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "for i in range(len(test_pts)):\n",
    "    if np.sign(w_decay_neg2.dot(transformed[i])) != out_labels[i]:\n",
    "        missclassified += 1\n",
    "e_out_decay_neg2 = missclassified / len(test_pts)\n",
    "\n",
    "(e_out_decay_2, e_out_decay_1, e_out_decay_0, e_out_decay_neg1, e_out_decay_neg2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.084, 0.084, 0.08, 0.084, 0.056, 0.092, 0.124, 0.228, 0.436, 0.452, 0.456]"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = [i for i in np.arange(-15,15,1, dtype=float)]\n",
    "out = []\n",
    "for i in range(30):\n",
    "    w_decay = np.asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "    x = regression_with_decay(pts, y, l[i])\n",
    "    w_decay += x[0]\n",
    "    \n",
    "    missclassified = 0\n",
    "    transformed = np.asarray(nonlinear_transform(test_pts))\n",
    "    for i in range(len(test_pts)):\n",
    "        if np.sign(w_decay.dot(transformed[i])) != out_labels[i]:\n",
    "            missclassified += 1\n",
    "    e_out_decay = missclassified / len(test_pts)\n",
    "    out.append(e_out_decay) \n",
    "plt.plot(l, out)\n",
    "out[10:21]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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