Ridge Regression - L2 Regularization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn import datasets\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setting_data(data=None):\n",
    "    feature_matrix = np.ones((np.ma.size(data,axis=0),np.ma.size(data,axis=1)+1))\n",
    "    feature_matrix[:,1:] = data\n",
    "    return feature_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_values(feature_matrix=None, weights=None):\n",
    "    return np.dot(a=feature_matrix,b=weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polynomial_features_generation(data=None, degree=0):\n",
    "    return np.hstack((data,np.power(data,np.arange(start=2,stop=degree+1))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standardization(data=None):\n",
    "    data = data.astype(float)\n",
    "    for i in range(data.shape[1]):\n",
    "        data[:,i] = np.divide(np.subtract(data[:,i],np.mean(data[:,i])), np.std(data[:,i])).astype(float)\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [],
   "source": [
    "def min_max_scaling(data=None):\n",
    "    data = data.astype(float)\n",
    "    for i in range(data.shape[1]):\n",
    "        min_ = np.min(data[:,i])\n",
    "        max_ = np.max(data[:,i])\n",
    "        max_minus_min = max_ - min_\n",
    "        data[:,i] = np.divide(np.subtract(data[:,i],min_),max_minus_min)\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [],
   "source": [
    "def root_mean_squared_error(y=None,y_bar=None,no_of_observations=0):\n",
    "    return np.sqrt(np.divide(np.sum(np.square(np.subtract(y,y_bar))),no_of_observations))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(x=None,y=None,tolerance_gradient=0.01, tolerance_cost=0.0000001,\n",
    "                     alpha = 0.001, max_iter=10000,l2_regularization=0):\n",
    "   \n",
    "    feature_matrix = setting_data(data=x)\n",
    "    \n",
    "    weights = np.random.rand(x.shape[1] + 1, 1)\n",
    "    partials = np.zeros(x.shape[1]+1).reshape((-1,1))\n",
    "    \n",
    "    i = 0\n",
    "    prev_cost = 10\n",
    "    costs = []\n",
    "    gradients = []\n",
    "    \n",
    "    converged = False\n",
    "    while not converged:\n",
    "        i += 1\n",
    "        \n",
    "        predicted = predict_values(feature_matrix=feature_matrix, weights=weights)\n",
    "        errors = np.subtract(predicted, y)\n",
    "        #Updating weights\n",
    "        \n",
    "        #taking derivative\n",
    "        partials = np.dot(feature_matrix.T,errors)\n",
    "        #This is the total change :p\n",
    "#         step_size = np.multiply(alpha,partials)\n",
    "#         weights_regularized = np.vstack((weights[0],np.multiply(weights[1:],1-2*alpha*l2_regularization)))\n",
    "        \n",
    "        weights = np.subtract(np.vstack((weights[0],np.multiply(weights[1:],1-2*alpha*l2_regularization))),\n",
    "                              np.multiply(alpha,partials))\n",
    "        \n",
    "        gradient_magnitude = np.sqrt(np.sum(np.square(partials)))\n",
    "        cur_cost = np.sum(np.square(errors))\n",
    "        \n",
    "#         gradients = np.append(gradients,gradient_magnitude)\n",
    "#         costs = np.append(costs,cur_cost)\n",
    "        gradients.append(gradient_magnitude)\n",
    "        costs.append(cur_cost)\n",
    "\n",
    "#         if i%1000==0:\n",
    "#             print(cur_cost)\n",
    "#         print(abs(cur_cost - prev_cost))\n",
    "        if (gradient_magnitude <= tolerance_gradient) or (abs(cur_cost - prev_cost) < tolerance_cost):\n",
    "            if gradient_magnitude <= tolerance_gradient:\n",
    "                print('[Gradient Magnitude - Tolerance] Satisfied')\n",
    "            else:\n",
    "                print('[Cost Tolerance - Precision] Satisfied')\n",
    "            converged = True\n",
    "\n",
    "        if i >= max_iter:\n",
    "            print('Iterations Completed')\n",
    "            converged = True\n",
    "        \n",
    "        prev_cost = cur_cost\n",
    "    return (i, np.array(weights),np.array(gradients), costs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-10, 11).reshape(-1,1)\n",
    "y = (10 + 2*x + 5*x**2).astype(float).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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fr+T1H/Zy6YAY+nUNtzuOy2mhPwMd2wXy83N7sHBrHhv3aQscpdzdK8v2UF5dyy8ntL2jeXCg0ItIkIisE5HNIrJdRP5ozU8UkbUikiEi80UkwJofaD3OsJYnOPcl2GPmeT3o1C6Qvy7cqXfLKuXG8oormLs6myuGxNGrczu749jCkSP6SmCcMWYQMBiYKCIjgb8BzxljegFHgNus9W8Djljzn7PW8zqhgX78ckIS67OOsGhHvt1xlFKN+Nf36RhjeODCJLuj2KbJQm/qHbce+ls/BhgHfGTNnwtMtaanWI+xlo8XL23HdG1KPD2iQnnq611U6yhUSrmdfYfLmL9+P9eeHU98ZIjdcWzj0Dl6EfEVkU1AAbAI2AMcNcbUWKvkACf6+YwF9gNYy4sBr7wzwc/Xh4cnJpNZWMr89fvtjqOUOsnzi3fj6yP8YlzbPZoHBwu9MabWGDMYiAOGA8kt3bCIzBSRVBFJLSwsbOmfs82Evl0YnhDJ89/t5nhlTdNPUEq5REZBCZ/9mMv00Ql0aR9kdxxbNavVjTHmKLAEGAVEiIiftSgOyLWmc4F4AGt5OPA/XT4aY2YZY1KMMSlRUZ47IK+I8MglyRw6XsWs5Zl2x1FKWZ5dtJuQAD/uHNvT7ii2c6TVTZSIRFjTwcAEYCf1Bf8qa7XpwOfW9ALrMdby742XN0sZ0q0Dlw6MYfbyTAqOVdgdR6k2b1tuMQu35jHjnEQiQwPsjmM7R47oY4AlIrIFWA8sMsZ8CfwWeFBEMqg/B/+6tf7rQEdr/oPAw60f2/385uLe1NTV8dx3ehOVUnZ75ts0woP9uf3cRLujuAW/plYwxmwBhpxifib15+tPnl8BXN0q6TxI946h3DiiO2+tzmLGmESSuoTZHUmpNmlDdhFL0gr57cRk2gf52x3HLeidsa3ovvFJhAb48bevd9kdRak2yRjD01+n0aldINNHd7c7jtvQQt+KIkMDuOuCnny3s4A1mTrkoFKu9kPGIdbuLeLeC3oSEtDkCYs2Qwt9K5sxJpGY8CCeXLiTujqvvgatlFsxxvCPb9KIjQjm+hHd7I7jVrTQt7Igf18euqg3W3KK+XLrQbvjKNVmLNqRz+acYu4fn0Sgn6/dcdyKFnonuGJILMnRYfz9m11U1tTaHUcpr1dXZ3h20W56dArlyqGxTT+hjdFC7wS+PsLvLunD/qJy3l6zz+44Snm9L7YcYFdeCQ9MOAs/Xy1rJ9M94iTnnRXFuUmd+Nf36RSXV9sdRymvVVFdyz++TSM5OozJA2LsjuOWtNA70cOTkikur9bxZZVyoleW7WF/UTmPXtYXHx+v7Ci3xbTQO1G/ruFcMSSWN1dmkXu03O44Snmd/UVlvLx0D5MHxjC6Zye747gtLfRO9tBFvQF45ps0m5Mo5X3++MUOfH2E31/ax+4obk0LvZPFRgQzY0win27KZVtusd1xlPIaS3YV8N3OfO4bn0RMeLDdcdyaFnoXuOv8nkQE+/PUV7t0fFmlWkFFdS2Pf7GdnlGhzBijHZc1RQu9C4QH+/OLcUn8kHGI5emH7I6jlMebvTyT7MNl/PHy/gT4aRlriu4hF7lpZHe6RYbw14U7qdWuEZQ6YzlHynhxaQaXDIjmnCS9AOsILfQuEuDnw68v7s2uvBI+2ZhjdxylPNYTX+5AEP7v0r52R/EYWuhdaPLAGAbFhfPMt7upqNauEZRqrmW7C/lmez73jutF1wi9AOsoLfQuVD++bB/yjlXw+g977Y6jlEeprKnl8QXbSewUqiNHNZMWehcb2aMjF/Xtwr++T2d/UZndcZTyGK+t2MveQ6U8fnk/7Z2ymbTQ2+Dxy/vhK8LvPt2qzS2VckDu0XL+/X0GF/frwtizouyO43G00Nuga0Qwv5mYzIr0Q3y2KdfuOEq5vb/8Zwd1xugF2DOkhd4mN43szpBuETzx5U6KSqvsjqOU2/oh/RALt+ZxzwW9iI8MsTuOR9JCbxNfH+GvVw7gWHk1f/7PDrvjKOWWqmrqeGzBNrp3DGHmeT3sjuOxtNDbKDm6PXeO7cknG3NZkV5odxyl3M6bK/eyp7CUxy7rS5C/XoA9U1robXbvuF706BTK7z/dRnmVtq1X6oS84gpeWJzOhX06My65i91xPJoWepsF+fvy5JUD2FdUxvOLd9sdRym38ZeFO6mpMzw6uZ/dUTyeFno3MLJHR65Niee1FXu1K2OlgFV7DvHF5gPcNbYn3TrqBdiW0kLvJn53SR86hATwyCdbtdMz1aZV19bx2OfbiY8M5q7ze9odxytooXcT4SH+PH55X7bmFvPmSu0eQbVdc1dlkV5wnEcn99MLsK1EC70buXRADOOSO/PMt7u1ewTVJhUcq+D579K5oHcUF/bpbHccr9FkoReReBFZIiI7RGS7iNxvzY8UkUUikm797mDNFxH5p4hkiMgWERnq7BfhLUSEJ6b2x0fg/z7bpt0jqDbnyYU769vOX9YPEbE7jtdw5Ii+BnjIGNMXGAncIyJ9gYeBxcaYJGCx9RhgEpBk/cwEXm711F4sNiKYX13cm2W7C1mw+YDdcZRymbWZh/ls0wHuGNuDhE6hdsfxKk0WemPMQWPMRmu6BNgJxAJTgLnWanOBqdb0FOAtU28NECEiMa2e3IvdPCqBQfER/OmLHRzR7hFUG1BZU8ujn28nNiKYu8/vZXccr9Osc/QikgAMAdYCXYwxB61FecCJOxpigf0NnpZjzVMO8vURnrpyAMXl1Ty5cKfdcZRyumcX7SYtv4Q/TelHcIBegG1tDhd6EWkHfAw8YIw51nCZqT+Z3KwTyiIyU0RSRSS1sFBv/z9Zn5j2zDyvBx9uyGFVhg4orrzX6j2HmbU8k+uHd2N8H70D1hkcKvQi4k99kX/HGPOJNTv/xCkZ63eBNT8XiG/w9Dhr3n8xxswyxqQYY1KiorR/6VO5b3wSCR1DeOTTrTr0oPJKxeXVPPTBJhI6hvKHyX3sjuO1HGl1I8DrwE5jzLMNFi0AplvT04HPG8y/2Wp9MxIobnCKRzVDkL8vT14xgOzDZfxzcbrdcZRqdY99vo38kkqeu3YwIQF+dsfxWo4c0Y8BpgHjRGST9XMJ8BQwQUTSgQutxwALgUwgA5gN3N36sduO0b06cfWwOGYtz2TnwWNNP0EpD/H5plw+23SA+8cnMTg+wu44Xk3coa12SkqKSU1NtTuG2zpaVsX4Z5YR1yGYT+4eg6+Pti9Wni33aDkTn19Or87t+PCOUfj56r2bZ0JENhhjUppaT/euB4gICeDRy/qyOaeYt1Zn2R1HqRapqzM89MEmausMz187WIu8C+ge9hCXD+rK+b2j+Ps3aeQeLbc7jlJn7LUfMlmTWcTjl/Wje0e9McoVtNB7CBHhz1P7Ywz8/tOt2j2C8kg7DhzjH9/s5uJ+Xbg6Jc7uOG2GFnoPEtchhN9O7M3StEJe/0F7uFSepaK6lgfm/0h4iD9/vXKg9mXjQlroPcz00Qlc3K8LT321i437jtgdRymHPf11Grvzj/P3qwYSGRpgd5w2RQu9hxERnr5qEDERQdz7zkbtC0d5hBXphbyxci/TR3Xn/N7a/bCraaH3QOHB/rx0wzAOHa/iwQ82UacjUik3drSsil99uJlendvx8CS9+9UOWug91IC4cP5vch+WpBXy6vJMu+ModUrGGH736VaKSqt4/trB2mGZTbTQe7BpI7tz6cAY/vFtGuuziuyOo9T/+GRjLgu35vHghN70jw23O06bpYXeg4nUd2fcLTKEe9/dyOHjlXZHUuon+4vKeGzBdoYnRjLzvB52x2nTtNB7uLAgf/59wxCOlFXzwHw9X6/cQ22d4ZfzNyHAs9cM0m47bKaF3gv06xrOHy/vx4r0Q7y4JMPuOErxyrI9pGYf4U9T+xHXIcTuOG2eFnovcd3Z8Uwd3JXnvtvNqj06UImyz9acYp5btJvJA2OYOlgHl3MHWui9hIjwlysGkNgplPve20RBSYXdkVQbVF5Vy/3zfyQqLJC/TB2gd7+6CS30XiQ00I+XbhzG8cpq7n+vvndApVzpyYU7ySws5ZmrBxEe4m93HGXRQu9lekeH8cSU/qzOPMwL3+22O45qQxZsPsC8Ndn8/NxERvfqZHcc1YAWei90dUo8Vw2L419LMli+WwdeV863IbuIX324meGJkfzq4t52x1En0ULvpZ6Y0p+zOofxwPxN5BXr+XrlPPsOlzHzrQ10DQ/i1ZuGEeind7+6Gy30Xio4wJcXbxxKRXUt9733IzW1dXZHUl6ouLyaGXPXU1NneOOWs+mgvVK6JS30XqxX53Y8ecUA1mUV8cwiPV+vWld1bR33vLOR7MOlvDptGD2i2tkdSTVCC72XmzokluuHd+PlpXv4fle+3XGUlzDG8Ojn2/gh4xBPXjGAkT062h1JnYYW+jbgscv60iemPQ9+sFnHm1Wt4rUVe3lv3X7uuaAnV6fE2x1HNUELfRsQ5O/LSzcOpabWcO+7G6msqbU7kvJg32zP48mvdnLpgBgemqAtbDyBFvo2IrFTKE9fNZAf9x3l/vc26cVZdUa25hTzwPubGBQXwTPXDMJHOyvzCFro25BLBsTw6OS+fL09j0c+2YoxeuesctzB4nJum7ueyNAAZt+cQpC/NqP0FH52B1CuNeOcRIrLq3lhcTrhwf78/tI+2h+JalJpZQ0z5qRSVlXLx3eNICos0O5Iqhm00LdBD1yYRHF5Na/9sJeIEH/uHZdkdyTlxmrrDPe99yO780t445az6R0dZnck1Uxa6NsgEeHRyX05Vl7NP77dTXiwP9NGJdgdS7mpv/xnJ4t3FfDE1P6MPSvK7jjqDGihb6N8fIS/XTWQYxU1PLpgO+2D/ZmifYerk8xbncUbK/cyY0wi00Z2tzuOOkNNXowVkTdEpEBEtjWYFykii0Qk3frdwZovIvJPEckQkS0iMtSZ4VXL+Pv68O8bhjAiMZKHPtisN1Sp/7I0rYDHv9jB+OTO/P7SPnbHUS3gSKubOcDEk+Y9DCw2xiQBi63HAJOAJOtnJvBy68RUzhLk78vsm1Po27U9d729kbWZh+2OpNxAWl4J9777I727hPHP64fomK8erslCb4xZDhSdNHsKMNeangtMbTD/LVNvDRAhIjGtFVY5R1iQP3NuHU5ch2Bun5vKttxiuyMpGxWUVDBjznpCAnx5/ZYUQgP1DK+nO9N29F2MMQet6TygizUdC+xvsF6ONU+5ucjQAN6+fQTtg/2Z/sY69hQetzuSskFFdS0/f2sDRaVVvD79bGLCg+2OpFpBi2+YMvV33TT7zhsRmSkiqSKSWliog2O4g5jwYN6+fQQiMO21tdovThtTUlHN9DfWsSXnKC9cN5gBceF2R1Kt5EwLff6JUzLW7wJrfi7QsIejOGve/zDGzDLGpBhjUqKitMmWu0jsFMrcGcMpqaxh2mtrOXS80u5IygUOHa/k+tlr2JB9hOevHcxF/aLtjqRa0ZkW+gXAdGt6OvB5g/k3W61vRgLFDU7xKA/Rr2s4b9xyNgeKy5n+xjqOVVTbHUk5Ue7Rcq55ZTUZBceZfXOKNrP1Qo40r3wPWA30FpEcEbkNeAqYICLpwIXWY4CFQCaQAcwG7nZKauV0ZydE8vJNw0jLK+H2OalUVGuPl94oo6CEq15eReHxSubdNoILkjvbHUk5gbhDx1YpKSkmNTXV7hjqFL7YfID73v+RC3p35tVpw/D31X7wvMXm/Ue55c11+Pr4MO+24fSJaW93JNVMIrLBGJPS1Hr6r1ad1mWDuvLnqf35flcBv/pwM3V19h8YqJZbmXGIG2avoV2QHx/fNUqLvJfTBrKqSTeO6E5xeTVPf51GRXUtz14zWNtWe7Cvtx3kvvc2kdgplLduG06X9kF2R1JOpkf0yiF3n9+LRyf3ZdGOfH728ir2F5XZHUmdgfnr93H3OxsZEBfOB3eM0iLfRmihVw6bcU4ib946nNyj5Ux5cSXr9p58w7RyZ68u28NvP97KuUlRzLttOOEh/nZHUi6ihV41y9izovj8njFEBPtz42treH/dPrsjqSYYY/jrVzv561e7uHxQV2bfnEJIgJ56a0u00Ktm6xHVjk/vGcOonp0dn8BrAAAMs0lEQVR4+JOt/PGL7ToGrZuqrTM88slWXl2WybSR3Xn+2sEE+Ok/+7ZG33F1RsKD/Xljegq3nZPImyuzuHXOeorL9MYqd1JZU8s972zk/fX7uW98En+a0k8H826jtNCrM+bn68MfJvfl6Z8NZE3mYaa+tJKMAu0MzR0cr6xhxpz1fL09j8cu68uDE87SsYHbMC30qsWuOTued38+kmPl1Vzx0kqWphU0/STlNEWlVdw4ew1rMot47tpB3Dom0e5IymZa6FWrODshkgW/OIe4DiHMmLOe11Zk4g53Xbc1S9MKuOSFFezKK2HWtGFcMSTO7kjKDWihV60mNiKYj+8axcX9ovnzf3by64+2UFmjfeS4QklFNY98soVb3lxPWJAfH905mvF9ujT9RNUmaBsr1apCAvx48YahvLA4nRcWp7P3UCmv3DSMqLBAu6N5rZUZh/jNR1s4WFzOnWN78sCFSQT5+9odS7kRPaJXrc7HR/jlhLN48YahbD9QzJR//6DDEzpBaWUNf/hsGze+tpZAPx8+vHM0D09K1iKv/ocWeuU0lw6M4aM7R2OAq19ZzXvr9lGrnaK1inV7i5j0wgreXpvNbeck8p/7zmVY9w52x1JuSgu9cqr+seEsuPccBsaF88gnW7n83z9o1wktUF5Vy5++2MG1s1YD8P7PR/KHyX0JDtCjeNU47Y9euYQxhgWbD/DUV7s4WFzBpQNieHhSMvGRIXZH8xgbso/w6w83k3molJtHdefhScnalUEb52h/9PopUS4hIkwZHMtFfaN5dfkeXlm2h0U787njvB7cObandnt8GhXVtTz33W5mL88kJjyYd24fwZheneyOpTyIHtErWxw4Ws5TX+1iweYDdGkfyG8nJjN1cKzeon+SLTlHeeiDzaQXHOf64fH87pI+hAVpr5OqnqNH9Frola02ZBfxxy92sCWnmEHxETx2WV+GdtOLilU1dfzr+3ReWrqHqHaB/O2qgYw9K8ruWMrNaKFXHqOuzvDJj7k8/fUuCkoqmTq4K7+dlExMeLDd0VyupKKajzfkMHd1NnsPlfKzoXE8ellfwoP1KF79Ly30yuOUVtbw0tIMZq/Yi68Id47tyczzerSJFiUZBceZtzqLjzbkUFpVy+D4CO4b34txyXp3q2qcFnrlsfYXlfHXr3aycGseXcODePiSPlw2MMbrel+srTMs2VXA3NVZrEg/RICvD5MHxjB9dAKD4iPsjqc8gBZ65fHWZB7mT1/sYMfBYyRHh3HpgBgmDYimV+cwu6O1yNGyKj5I3c+8NdnsLyonun0QN43sxnXDu9GpnXYVoRynhV55hdo6w8cbcpifup8N2UcASOrcjkn9o5nYP4Y+MWEec6S/8+Ax5q7K4rNNuVRU1zE8MZJbRicwoW8X/H313kXVfFroldfJK67gm+15fLXtIOv2FlFnoHvHECb2j2ZS/xgGxYW7XdGvrq1j0Y585qzKYt3eIoL8fbhiSCzTRibQt2t7u+MpD6eFXnm1Q8crWbQjn6+25bEq4xA1dYbYiGAu7hfNpAHRDOvWwZY2+XV1htyj5aTllbAl5ygfpOaQd6yCuA7B3DyqO9ekxBMREuDyXMo7aaFXbUZxWTWLdubz9baDLE8/RFVNHVFhgVzcrwuT+scwIjESPyecGikqrWJX3jF255WQll/CrrwSdueVUFr1//vgPzepE9NHJXBBcmd89WYw1cq00Ks26XhlDd/vKuDrbQdZsquQ8upaAv18iAwNICIkgA4h/nQItX6HNJgXEvDT/IiQANoH+f10Gqi8qpb0gvpCnpZXwm6rqBeWVP603YgQf3p3CaN3dP1PcnQYSV3CaK93sSon0r5uVJvULtCPywd15fJBXSmvqmXZ7kI27jtCUWkVR8uqOFJWzc6DxzhSWkVxeTWN9Zrs6yNEBPsT5O/LgeJyThwPBfr5kNSlHeclRZEcHcZZVlHvHBbodtcHlDrBKYVeRCYCLwC+wGvGmKecsR2lTic4wJeJ/aOZ2D/6lMvr6gzHKqo5UlbNkbIqjpTWfxHUfyHUT5dV1tC9YxzJ1pF6946hegpGeZxWL/Qi4gu8CEwAcoD1IrLAGLOjtbelVEv4+AgR1umbRELtjqOU0zij8e5wIMMYk2mMqQLeB6Y4YTtKKaUc4IxCHwvsb/A4x5qnlFLKBrbdjiciM0UkVURSCwsL7YqhlFJezxmFPheIb/A4zpr3X4wxs4wxKcaYlKgo7WdbKaWcxRmFfj2QJCKJIhIAXAcscMJ2lFJKOaDVW90YY2pE5F7gG+qbV75hjNne2ttRSinlGKe0ozfGLAQWOuNvK6WUah7tG1UppbycW/R1IyKFQPYZPr0TcKgV47QWzdU8mqv53DWb5mqeluTqboxpsjWLWxT6lhCRVEc69XE1zdU8mqv53DWb5moeV+TSUzdKKeXltNArpZSX84ZCP8vuAI3QXM2juZrPXbNpruZxei6PP0evlFLq9LzhiF4ppdRpeEShF5GrRWS7iNSJSMpJyx4RkQwRSRORixt5fqKIrLXWm291zdDaGeeLyCbrJ0tENjWyXpaIbLXWc/r4iSLyuIjkNsh2SSPrTbT2YYaIPOyCXH8XkV0iskVEPhWRiEbWc8n+aur1i0ig9R5nWJ+lBGdlabDNeBFZIiI7rM///adY53wRKW7w/j7q7FzWdk/7vki9f1r7a4uIDHVBpt4N9sMmETkmIg+ctI7L9peIvCEiBSKyrcG8SBFZJCLp1u8OjTx3urVOuohMb3EYY4zb/wB9gN7AUiClwfy+wGYgEEgE9gC+p3j+B8B11vQrwF1OzvsM8Ggjy7KATi7cd48Dv2piHV9r3/UAAqx92tfJuS4C/KzpvwF/s2t/OfL6gbuBV6zp64D5LnjvYoCh1nQYsPsUuc4HvnTV58nR9wW4BPgKEGAksNbF+XyBPOrbmduyv4DzgKHAtgbzngYetqYfPtXnHogEMq3fHazpDi3J4hFH9MaYncaYtFMsmgK8b4ypNMbsBTKoH/jkJ1I/kOc44CNr1lxgqrOyWtu7BnjPWdtwApcPFmOM+dYYU2M9XEN9L6d2ceT1T6H+swP1n6Xx4uRBYo0xB40xG63pEmAnnjO2wxTgLVNvDRAhIjEu3P54YI8x5kxvxGwxY8xyoOik2Q0/R43VoouBRcaYImPMEWARMLElWTyi0J+GI4OcdASONigqzh4I5Vwg3xiT3shyA3wrIhtEZKYTczR0r/Xf5zca+a+i3YPFzKD+6O9UXLG/HHn9P61jfZaKqf9suYR1qmgIsPYUi0eJyGYR+UpE+rkoUlPvi92fqeto/GDLjv11QhdjzEFrOg/ocop1Wn3fOaVTszMhIt8BpxrF+ffGmM9dnedUHMx4Pac/mj/HGJMrIp2BRSKyy/rmd0ou4GXgCer/YT5B/WmlGS3ZXmvkOrG/ROT3QA3wTiN/ptX3l6cRkXbAx8ADxphjJy3eSP3piePW9ZfPgCQXxHLb98W6Bnc58MgpFtu1v/6HMcaIiEuaPbpNoTfGXHgGT3NkkJPD1P+30c86EjvlQCitkVFE/IArgWGn+Ru51u8CEfmU+tMGLfoH4ui+E5HZwJenWOTQYDGtnUtEbgEmA+ONdXLyFH+j1ffXKTjy+k+sk2O9z+HUf7acSkT8qS/y7xhjPjl5ecPCb4xZKCIviUgnY4xT+3Rx4H1xymfKQZOAjcaY/JMX2LW/GsgXkRhjzEHrVFbBKdbJpf5awglx1F+fPGOefupmAXCd1SIikfpv5nUNV7AKyBLgKmvWdMBZ/0O4ENhljMk51UIRCRWRsBPT1F+Q3HaqdVvLSedFr2hkey4fLEZEJgK/AS43xpQ1so6r9pcjr38B9Z8dqP8sfd/Yl1Nrsa4BvA7sNMY828g60SeuFYjIcOr/TTv1C8jB92UBcLPV+mYkUNzglIWzNfq/ajv210kafo4aq0XfABeJSAfrVOtF1rwz54qrzy39ob5A5QCVQD7wTYNlv6e+xUQaMKnB/IVAV2u6B/VfABnAh0Cgk3LOAe48aV5XYGGDHJutn+3Un8Jw9r6bB2wFtlgfspiTc1mPL6G+VcceF+XKoP485Cbr55WTc7lyf53q9QN/ov6LCCDI+uxkWJ+lHi7YR+dQf8ptS4P9dAlw54nPGXCvtW82U39Re7QLcp3yfTkplwAvWvtzKw1ayzk5Wyj1hTu8wTxb9hf1XzYHgWqrft1G/XWdxUA68B0Qaa2bArzW4LkzrM9aBnBrS7PonbFKKeXlPP3UjVJKqSZooVdKKS+nhV4ppbycFnqllPJyWuiVUsrLaaFXSikvp4VeKaW8nBZ6pZTycv8PWun4jUTp2pEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating Polynomial Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.6514456477]\n",
      " [-1.4863010829]\n",
      " [-1.3211565182]\n",
      " [-1.1560119534]\n",
      " [-0.9908673886]\n",
      " [-0.8257228238]\n",
      " [-0.6605782591]\n",
      " [-0.4954336943]\n",
      " [-0.3302891295]\n",
      " [-0.1651445648]\n",
      " [ 0.          ]\n",
      " [ 0.1651445648]\n",
      " [ 0.3302891295]\n",
      " [ 0.4954336943]\n",
      " [ 0.6605782591]\n",
      " [ 0.8257228238]\n",
      " [ 0.9908673886]\n",
      " [ 1.1560119534]\n",
      " [ 1.3211565182]\n",
      " [ 1.4863010829]\n",
      " [ 1.6514456477]]\n",
      "[[20.333472341 ]\n",
      " [18.0728523796]\n",
      " [16.084959691 ]\n",
      " [14.3697942751]\n",
      " [12.9273561319]\n",
      " [11.7576452614]\n",
      " [10.8606616637]\n",
      " [10.2364053387]\n",
      " [ 9.8848762864]\n",
      " [ 9.8060745068]\n",
      " [10.          ]\n",
      " [10.4666527659]\n",
      " [11.2060328045]\n",
      " [12.2181401159]\n",
      " [13.5029747   ]\n",
      " [15.0605365568]\n",
      " [16.8908256863]\n",
      " [18.9938420886]\n",
      " [21.3695857636]\n",
      " [24.0180567113]\n",
      " [26.9392549317]]\n"
     ]
    }
   ],
   "source": [
    "x_norm = standardization(x)\n",
    "y_norm = (10 + 2*x_norm + 5*x_norm**2).reshape(-1,1)\n",
    "print(x_norm)\n",
    "print(y_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [],
   "source": [
    "degree = 2\n",
    "x_poly = polynomial_features_generation(x_norm,degree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Cost Tolerance - Precision] Satisfied\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "i,cal_weights, grads, costs = gradient_descent(x=x_poly, y=y_norm,alpha=1e-5,tolerance_cost=1e-7,\n",
    "                                               tolerance_gradient=1e-7, max_iter=1e7)\n",
    "end_time = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken:  4.700448989868164\n",
      "Iterations:  91091\n",
      "Calculated weights:\n",
      " [[9.991328727 ]\n",
      " [1.9999999927]\n",
      " [5.0058856294]]\n"
     ]
    }
   ],
   "source": [
    "print('Time taken: ',end_time-start_time)\n",
    "print('Iterations: ',i)\n",
    "print('Calculated weights:\\n',cal_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orignal weights were: 10    2    5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fc2e61b5748>"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = (cal_weights[0] + cal_weights[1]*x_norm + cal_weights[2]*x_norm**2).reshape(-1,1)\n",
    "\n",
    "sns.lineplot(x=x_norm[:,0],y=y_norm[:,0],color='g')\n",
    "sns.scatterplot(x=x_norm[:,0],y=result[:,0],color='b')"
   ]
  },
  {
   "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": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Running on real dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [],
   "source": [
    "house_data = pd.read_csv('Related Datasets/kc_house_data.csv')\n",
    "house_test_data = pd.read_csv('Related Datasets/kc_house_test_data.csv')\n",
    "house_train_data = pd.read_csv('Related Datasets/kc_house_train_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array(house_train_data['sqft_living']).reshape(-1,1)\n",
    "target = np.array(house_train_data['price']).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "standardizing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(17384, 1)\n",
      "(17384, 1)\n"
     ]
    }
   ],
   "source": [
    "data = min_max_scaling(data)\n",
    "print(data.shape)\n",
    "print(target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {},
   "outputs": [],
   "source": [
    "max = np.max(data)\n",
    "index_max = np.argmax(data)\n",
    "data = np.delete(data,index_max).reshape(-1,1)\n",
    "target_not_shaped = np.delete(target,index_max)\n",
    "target = target_not_shaped.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(17383, 1)\n",
      "(17383, 1)\n",
      "(17383,)\n"
     ]
    }
   ],
   "source": [
    "print(data.shape)\n",
    "print(target.shape)\n",
    "print(target_not_shaped.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating polynomail features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17383, 4)"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_poly = polynomial_features_generation(data,4)\n",
    "data_poly.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with small lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations Completed\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "i,weights_l2_0, grads, costs = gradient_descent(x=data, y=target,alpha=1e-12,tolerance_cost=1e-7,\n",
    "                                               tolerance_gradient=1e-7, max_iter=10000,l2_regularization=0)\n",
    "end_time = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken:  1.40938401222229\n",
      "Iterations:  10000\n",
      "Calculated weights:\n",
      " [[93.8991471426]\n",
      " [45.8077908928]]\n"
     ]
    }
   ],
   "source": [
    "print('Time taken: ',end_time-start_time)\n",
    "print('Iterations: ',i)\n",
    "np.set_printoptions(precision=10)\n",
    "print('Calculated weights:\\n',weights_l2_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With big lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations Completed\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "i,weights_l2_1e11, grads, costs = gradient_descent(x=data, y=target,alpha=1e-12,tolerance_cost=1e-7,\n",
    "                                               tolerance_gradient=1e-7, max_iter=10000,l2_regularization=1e11)\n",
    "end_time = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken:  1.4404230117797852\n",
      "Iterations:  10000\n",
      "Calculated weights:\n",
      " [[9.4081078988e+01]\n",
      " [2.2444800404e-02]]\n"
     ]
    }
   ],
   "source": [
    "print('Time taken: ',end_time-start_time)\n",
    "print('Iterations: ',i)\n",
    "np.set_printoptions(precision=10)\n",
    "print('Calculated weights:\\n',weights_l2_1e11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fc3942668d0>"
      ]
     },
     "execution_count": 330,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "result_l2_0 = weights_l2_0[0] + weights_l2_0[1]*data[:,0]\n",
    "temp_df_small_l2 = pd.DataFrame(data,columns=['sqft'])\n",
    "temp_df_small_l2['predicted_price'] = result_l2_0\n",
    "sns.scatterplot(data=temp_df_small_l2,x=data[:,0],y='predicted_price',color='r')\n",
    "\n",
    "result_l2_1e11 = weights_l2_1e11[0] + weights_l2_1e11[1]*data[:,0]\n",
    "temp_df_big_l2 = pd.DataFrame(data,columns=['sqft'])\n",
    "temp_df_big_l2['predicted_price'] = result_l2_1e11\n",
    "sns.scatterplot(data=temp_df_big_l2,x=data[:,0],y='predicted_price',color='b')\n",
    "\n",
    "sns.scatterplot(x=data[:,0],y=target_not_shaped,color='g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 0 l2:    86174786.46180694\n",
      "For 1e12 l2: 86174762.90283266\n"
     ]
    }
   ],
   "source": [
    "print('For 0 l2:   ',root_mean_squared_error(result_l2_0,target,target.shape[0]))\n",
    "print('For 1e12 l2:',root_mean_squared_error(result_l2_1e11,target,target.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y_true</th>\n",
       "      <th>y_pred_no_reg</th>\n",
       "      <th>y_pred_reg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>221900.0</td>\n",
       "      <td>49.163722</td>\n",
       "      <td>94.059160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>538000.0</td>\n",
       "      <td>118.252835</td>\n",
       "      <td>94.093012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>180000.0</td>\n",
       "      <td>28.784919</td>\n",
       "      <td>94.049174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>604000.0</td>\n",
       "      <td>87.933153</td>\n",
       "      <td>94.078156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>510000.0</td>\n",
       "      <td>74.015921</td>\n",
       "      <td>94.071337</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     y_true  y_pred_no_reg  y_pred_reg\n",
       "0  221900.0      49.163722   94.059160\n",
       "1  538000.0     118.252835   94.093012\n",
       "2  180000.0      28.784919   94.049174\n",
       "3  604000.0      87.933153   94.078156\n",
       "4  510000.0      74.015921   94.071337"
      ]
     },
     "execution_count": 332,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'y_true': target[:,0], 'y_pred_no_reg': result_l2_0, 'y_pred_reg': result_l2_1e11})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/nauman/.local/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fc3917010b8>"
      ]
     },
     "execution_count": 333,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x=temp_df_big_l2['sqft'],y=temp_df_big_l2['predicted_price'],color='b')\n",
    "sns.lineplot(x=temp_df_small_l2['sqft'],y=temp_df_small_l2['predicted_price'],color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With polynomial features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Small lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations Completed\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "i,weights_l2_0, grads, costs = gradient_descent(x=data_poly, y=target,alpha=1e-12,tolerance_cost=1e-7,\n",
    "                                               tolerance_gradient=1e-7, max_iter=10000,l2_regularization=0)\n",
    "end_time = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken:  1.4229323863983154\n",
      "Iterations:  10000\n",
      "Calculated weights:\n",
      " [[  92.9749595205]\n",
      " [  39.693544375 ]\n",
      " [ 150.7661367723]\n",
      " [ 346.6097260537]\n",
      " [1151.8851133261]]\n"
     ]
    }
   ],
   "source": [
    "print('Time taken: ',end_time-start_time)\n",
    "print('Iterations: ',i)\n",
    "np.set_printoptions(precision=10)\n",
    "print('Calculated weights:\\n',weights_l2_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With big lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations Completed\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "i,weights_l2_1e11, grads, costs = gradient_descent(x=data_poly, y=target,alpha=1e-12,tolerance_cost=1e-7,\n",
    "                                               tolerance_gradient=1e-7, max_iter=10000,l2_regularization=1e11)\n",
    "end_time = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken:  1.7050368785858154\n",
      "Iterations:  10000\n",
      "Calculated weights:\n",
      " [[9.3890344154e+01]\n",
      " [2.2438620980e-02]\n",
      " [9.4232991969e-02]\n",
      " [3.2176690579e-01]\n",
      " [1.8810667037e+00]]\n"
     ]
    }
   ],
   "source": [
    "print('Time taken: ',end_time-start_time)\n",
    "print('Iterations: ',i)\n",
    "print('Calculated weights:\\n',weights_l2_1e11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/nauman/.local/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fc3921c60b8>"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "result_l2_0 = weights_l2_0[0] + weights_l2_0[1]*data_poly[:,0] + weights_l2_0[2]*data_poly[:,1] + weights_l2_0[3]*data_poly[:,2]+ weights_l2_0[4]*data_poly[:,3]\n",
    "# temp_df_small_l2 = pd.DataFrame(data_poly,columns=[['sqft_1','sqft_2','sqft_3','sqft_4']])\n",
    "# temp_df_small_l2['predicted_price'] = result_l2_0\n",
    "sns.lineplot( x=data_poly[:,0], y=result_l2_0,color='r')\n",
    "\n",
    "result_l2_1e11 = weights_l2_1e11[0] + weights_l2_1e11[1]*data_poly[:,0]  + weights_l2_1e11[2]*data_poly[:,1]  + weights_l2_1e11[3]*data_poly[:,2]  + weights_l2_1e11[4]*data_poly[:,3]\n",
    "# temp_df_big_l2 = pd.DataFrame(data_poly,columns=[['sqft_1','sqft_2','sqft_3','sqft_4']])\n",
    "# temp_df_big_l2['predicted_price'] = result_l2_1e11\n",
    "sns.lineplot(x=data_poly[:,0],y=result_l2_1e11,color='b')\n",
    "\n",
    "sns.scatterplot(x=data_poly[:,0],y=target_not_shaped,color='g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}