06 - Linear Regression/Application of derivative.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "d1410a6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = lambda x : 6*x**2 + 2*x + 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "939ff89f",
   "metadata": {},
   "outputs": [],
   "source": [
    "der = lambda x : 12*x + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "646854bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.001\n",
    "cur_x = (10)\n",
    "change = 1\n",
    "iteration = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "08d2d97d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.1583677969489354 -0.1584673833855482 9.958643661278632e-05\n",
      "9.833736702811278\n"
     ]
    }
   ],
   "source": [
    "minimal = []\n",
    "x_value = []\n",
    "change__ = []\n",
    "while abs(change) > 0.0001:\n",
    "    #print(y(cur_x))\n",
    "    minimal.append(y(cur_x))\n",
    "    x_value.append(cur_x)\n",
    "    prev_x = cur_x\n",
    "    cur_x = cur_x - der(cur_x) * lr\n",
    "    change = prev_x - cur_x\n",
    "    #print(prev_x, cur_x, change)\n",
    "    change__.append(change)\n",
    "print(prev_x, cur_x, change)    \n",
    "print(y(cur_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10e23d71",
   "metadata": {},
   "outputs": [],
   "source": [
    "minimal = []\n",
    "x_value = []\n",
    "change__ = []\n",
    "while iteration > 0:\n",
    "    #print(y(cur_x))\n",
    "    minimal.append(y(cur_x))\n",
    "    x_value.append(cur_x)\n",
    "    prev_x = cur_x\n",
    "    cur_x = cur_x - der(cur_x) * lr\n",
    "    change = prev_x - cur_x\n",
    "    #print(prev_x, cur_x, change)\n",
    "    change__.append(change)\n",
    "    iteration = iteration - 1\n",
    "print(prev_x, cur_x, change)    \n",
    "print(y(cur_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "24969724",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1584673833855482"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cur_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "92469d9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.833736702811278"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y(cur_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "f40ebdf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "2a62571c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbec8cf0610>]"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(minimal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "5f16c49e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbec8d4f250>]"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "c88e9aa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.DataFrame(change__).plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cff7cef6",
   "metadata": {},
   "source": [
    "# we have found the value of x where y function is minimal\n",
    "# using first order derivative iterative methodology to optimize the minimal value of a function y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "496832e5",
   "metadata": {},
   "source": [
    "6 * x**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3949a2be",
   "metadata": {},
   "source": [
    "First order derivative - 12*x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e94ab41",
   "metadata": {},
   "source": [
    "second order derivative - 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50d38e66",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "609423ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "MSE = 1/n(summation(y-ycap)^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb4eaff8",
   "metadata": {},
   "outputs": [],
   "source": [
    "Partial Derivative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31634359",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 5*x**2 + 2*x + 3*x*z +10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "334b59b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "partial derivative on x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10493114",
   "metadata": {},
   "outputs": [],
   "source": [
    "10*x + 2 + 3*z "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b6edbb49",
   "metadata": {},
   "outputs": [],
   "source": [
    "partial derivative on z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42067fcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "0 + 0 + 3*x + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33109d8b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7da5ba18",
   "metadata": {},
   "outputs": [],
   "source": [
    "3*x**2 + 2*x + 3*z**2 + 3*z + 3 *x**2*z + z + 10 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d40f5aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "partial derivative on x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9ebdba9",
   "metadata": {},
   "outputs": [],
   "source": [
    "6*x + 2 + 0 + 0 + 6*x*z + 0 + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e5d2a43",
   "metadata": {},
   "outputs": [],
   "source": [
    "partial derivative on z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d3a3ae0",
   "metadata": {},
   "outputs": [],
   "source": [
    "0 + 0 +6*z + 3 + 3*x**2 + 1 + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "30664528",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec6f5349",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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