Gradient Descent - Optimization .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0b68f831",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a8122868",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "X, y = make_classification(n_samples=100, n_features=2, n_informative=1,n_redundant=0,\n",
    "                           n_classes=2, n_clusters_per_class=1, random_state=41,hypercube=False,class_sep=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3a8d55f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cb8af586",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x295167f8dc0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.scatter(X[:,0],X[:,1],c=y,cmap='winter',s=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ca4bd5f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:1173: FutureWarning: `penalty='none'`has been deprecated in 1.2 and will be removed in 1.4. To keep the past behaviour, set `penalty=None`.\n",
      "  warnings.warn(\n",
      "C:\\Users\\Admin\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:350: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(penalty=&#x27;none&#x27;, solver=&#x27;sag&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(penalty=&#x27;none&#x27;, solver=&#x27;sag&#x27;)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(penalty='none', solver='sag')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "LR = LogisticRegression(penalty='none',solver='sag')\n",
    "LR.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd516873",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.81655966 0.21740956]]\n",
      "[5.78887383]\n"
     ]
    }
   ],
   "source": [
    "print(LR.coef_)\n",
    "print(LR.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2fca7a22",
   "metadata": {},
   "outputs": [],
   "source": [
    "m1 = -(LR.coef_[0][0]/LR.coef_[0][1])\n",
    "b1 = -(LR.intercept_/LR.coef_[0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b1c61645",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_input = np.linspace(-3,3,100)\n",
    "y_input = m1*x_input + b1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e30f39d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gd(X,y):\n",
    "    \n",
    "    X = np.insert(X,0,1,axis=1)\n",
    "    weights = np.ones(X.shape[1])\n",
    "    lr = 0.5\n",
    "    \n",
    "    for i in range(5000):\n",
    "        y_hat = sigmoid(np.dot(X,weights))\n",
    "        weights = weights + lr*(np.dot((y-y_hat),X)/X.shape[0])\n",
    "        \n",
    "    return weights[1:],weights[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2d0f0a98",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9b1ae99e",
   "metadata": {},
   "outputs": [],
   "source": [
    "coef_,intercept_ = gd(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ed49a667",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = -(coef_[0]/coef_[1])\n",
    "b = -(intercept_/coef_[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "240dfd8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_input1 = np.linspace(-3,3,100)\n",
    "y_input1 = m*x_input1 + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "82739221",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.0, 2.0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.plot(x_input,y_input,color='red',linewidth=3)\n",
    "plt.plot(x_input1,y_input1,color='black',linewidth=3)\n",
    "plt.scatter(X[:,0],X[:,1],c=y,cmap='winter',s=100)\n",
    "plt.ylim(-3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0d75c3d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.51123145, -0.11697552],\n",
       "       [ 1.        ,  0.06316371, -0.73115232],\n",
       "       [ 1.        , -0.0425064 , -0.7081059 ],\n",
       "       [ 1.        , -3.2891569 , -2.01199214],\n",
       "       [ 1.        ,  0.1111445 ,  1.63493163],\n",
       "       [ 1.        , -2.53070306,  0.15599044],\n",
       "       [ 1.        , -3.49036198,  1.07782053],\n",
       "       [ 1.        ,  0.3976447 ,  0.80626713],\n",
       "       [ 1.        , -0.24666899,  0.74859527],\n",
       "       [ 1.        , -3.65803446,  0.75152794],\n",
       "       [ 1.        , -3.47658131, -0.90114581],\n",
       "       [ 1.        , -3.47815037, -0.1815243 ],\n",
       "       [ 1.        ,  0.29004249, -2.98092432],\n",
       "       [ 1.        ,  1.11761831,  1.20500136],\n",
       "       [ 1.        , -3.52530398,  0.78302407],\n",
       "       [ 1.        ,  0.69929128,  0.42968688],\n",
       "       [ 1.        ,  0.17089733, -0.73229726],\n",
       "       [ 1.        , -3.57785124, -0.83930476],\n",
       "       [ 1.        ,  0.12965489,  0.83727062],\n",
       "       [ 1.        , -3.46888717, -0.10255323],\n",
       "       [ 1.        , -3.97487212,  0.65867001],\n",
       "       [ 1.        , -3.76348686,  0.92649819],\n",
       "       [ 1.        , -3.01519735,  0.10216193],\n",
       "       [ 1.        ,  1.92241659,  0.46886454],\n",
       "       [ 1.        , -2.91479578,  0.45432938],\n",
       "       [ 1.        ,  0.9259563 ,  1.8613386 ],\n",
       "       [ 1.        , -3.4859014 , -0.79255991],\n",
       "       [ 1.        , -2.73978345, -1.0004391 ],\n",
       "       [ 1.        , -4.09896768, -0.53814137],\n",
       "       [ 1.        , -3.50212636,  0.44027716],\n",
       "       [ 1.        , -3.13904797,  0.27047889],\n",
       "       [ 1.        ,  1.66188378, -0.75869267],\n",
       "       [ 1.        ,  0.53718567,  0.6802322 ],\n",
       "       [ 1.        ,  0.84886927,  0.17018845],\n",
       "       [ 1.        ,  0.86681859, -1.01121977],\n",
       "       [ 1.        , -0.00979785, -0.8394709 ],\n",
       "       [ 1.        , -2.68650432,  0.90327412],\n",
       "       [ 1.        ,  0.98593205,  1.16981747],\n",
       "       [ 1.        , -3.30742775,  0.53461406],\n",
       "       [ 1.        ,  1.06925594, -0.22100631],\n",
       "       [ 1.        , -3.0242056 , -0.64584571],\n",
       "       [ 1.        , -2.61612476,  0.21243302],\n",
       "       [ 1.        , -3.05407331,  0.98654083],\n",
       "       [ 1.        ,  1.78068059,  0.67382928],\n",
       "       [ 1.        , -2.50369897, -0.11323563],\n",
       "       [ 1.        ,  1.39258216,  0.91694693],\n",
       "       [ 1.        ,  0.45865727,  0.3645213 ],\n",
       "       [ 1.        , -3.07153732, -0.78470874],\n",
       "       [ 1.        , -2.79571273, -1.48004137],\n",
       "       [ 1.        , -2.6184666 ,  0.72931763],\n",
       "       [ 1.        ,  0.53218913, -0.60000139],\n",
       "       [ 1.        , -0.0395452 ,  0.14720034],\n",
       "       [ 1.        , -3.11964851,  0.35215601],\n",
       "       [ 1.        ,  1.2561371 ,  0.17388705],\n",
       "       [ 1.        ,  2.45686591, -0.17162755],\n",
       "       [ 1.        , -3.2252872 ,  0.03763193],\n",
       "       [ 1.        ,  1.3467772 ,  0.48360467],\n",
       "       [ 1.        , -3.75380319, -0.07909256],\n",
       "       [ 1.        , -3.03070579,  0.06158897],\n",
       "       [ 1.        ,  0.20583358, -1.20413846],\n",
       "       [ 1.        ,  1.21108994,  0.77324391],\n",
       "       [ 1.        , -3.01981877,  0.7640092 ],\n",
       "       [ 1.        , -3.66318854,  1.57200032],\n",
       "       [ 1.        ,  1.28298186,  0.47296516],\n",
       "       [ 1.        ,  0.3640611 ,  0.0642074 ],\n",
       "       [ 1.        , -0.35195584,  1.52469135],\n",
       "       [ 1.        , -3.59205904, -2.1450828 ],\n",
       "       [ 1.        ,  0.9061286 , -0.7701428 ],\n",
       "       [ 1.        , -3.25090707,  0.84455766],\n",
       "       [ 1.        , -2.69817214,  1.29753064],\n",
       "       [ 1.        , -4.09493435, -0.84276652],\n",
       "       [ 1.        ,  0.58735838,  2.0615874 ],\n",
       "       [ 1.        ,  1.3843216 , -0.3036533 ],\n",
       "       [ 1.        , -3.15603064, -0.1656085 ],\n",
       "       [ 1.        ,  1.37865857,  1.16969713],\n",
       "       [ 1.        ,  0.98696744, -0.3038555 ],\n",
       "       [ 1.        , -3.88083743, -0.4788978 ],\n",
       "       [ 1.        ,  1.27593515,  0.28128262],\n",
       "       [ 1.        , -3.01387754,  0.70412341],\n",
       "       [ 1.        ,  1.0278443 ,  0.3757601 ],\n",
       "       [ 1.        ,  0.15011746,  0.97247545],\n",
       "       [ 1.        ,  1.653853  ,  0.56868381],\n",
       "       [ 1.        , -3.15852226, -0.39767934],\n",
       "       [ 1.        ,  1.68843893, -1.08933729],\n",
       "       [ 1.        , -0.04572327, -1.81663939],\n",
       "       [ 1.        , -3.56234524,  1.41775924],\n",
       "       [ 1.        , -3.48093864,  0.27098296],\n",
       "       [ 1.        , -2.88757001, -0.56186639],\n",
       "       [ 1.        ,  0.57853245,  0.42168159],\n",
       "       [ 1.        , -2.98638242, -2.95373116],\n",
       "       [ 1.        ,  1.06361882,  0.19492133],\n",
       "       [ 1.        ,  1.47452652, -0.04578681],\n",
       "       [ 1.        , -2.8571924 , -0.18860967],\n",
       "       [ 1.        , -3.18522871,  0.44635682],\n",
       "       [ 1.        ,  1.06491218, -1.49814775],\n",
       "       [ 1.        , -3.82161901,  0.66198774],\n",
       "       [ 1.        , -3.23429001,  0.07153265],\n",
       "       [ 1.        , -3.15863898,  0.32323638],\n",
       "       [ 1.        ,  1.14824982, -0.34574201],\n",
       "       [ 1.        ,  0.04627774,  0.06499922]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.insert(X,0,1,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "eedecd2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1 = np.insert(X,0,1,axis=1)\n",
    "np.ones(X1.shape[1])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
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