machinelearning

CustomLinearRegression.ipynb (82599B)

---

 {
  "cells": [
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Three approaches to linear regression:\n",
     "\n",
     "Mean Error\n",
     "\n",
     "Square Mean Error\n",
     "\n",
     "Matrix"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 484,
    "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
     "# Generate data\n",
     "\n",
     "X = np.linspace(0,20,1000)\n",
     "y = (X * 2.53) + np.random.randn(1000) * 10"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 485,
    "metadata": {},
    "outputs": [
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           "scene": {
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             "gridcolor": "white",
             "gridwidth": 2,
             "linecolor": "white",
             "showbackground": true,
             "ticks": "",
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             "gridcolor": "white",
             "gridwidth": 2,
             "linecolor": "white",
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             "gridwidth": 2,
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             "linecolor": "white",
             "ticks": ""
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            "bgcolor": "#E5ECF6",
            "caxis": {
             "gridcolor": "white",
             "linecolor": "white",
             "ticks": ""
            }
           },
           "title": {
            "x": 0.05
           },
           "xaxis": {
            "automargin": true,
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": "",
            "title": {
             "standoff": 15
            },
            "zerolinecolor": "white",
            "zerolinewidth": 2
           },
           "yaxis": {
            "automargin": true,
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": "",
            "title": {
             "standoff": 15
            },
            "zerolinecolor": "white",
            "zerolinewidth": 2
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         "xaxis": {
          "anchor": "y",
          "domain": [
           0,
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          "title": {
           "text": "x"
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         "yaxis": {
          "anchor": "x",
          "domain": [
           0,
           1
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          "title": {
           "text": "y"
          }
         }
        }
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "import plotly.express as px\n",
     "\n",
     "px.scatter(x=X,y=y)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Custom Implementation #1:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 486,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "2.5698125291111236"
       ]
      },
      "execution_count": 486,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "coeff = 0\n",
     "\n",
     "x_sum = 0\n",
     "y_sum = 0\n",
     "\n",
     "for i in range(0,len(X)):\n",
     "    x_sum += X[i]\n",
     "    y_sum += y[i]\n",
     "\n",
     "coeff = y_sum/x_sum\n",
     "\n",
     "coeff"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Custom Implementation #2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 487,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "2.7039711370725312"
       ]
      },
      "execution_count": 487,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "coeff = 0\n",
     "\n",
     "x_sum = 0\n",
     "y_sum = 0\n",
     "\n",
     "for i in range(0,len(X)):\n",
     "    x_sum += X[i] * X[i]\n",
     "    y_sum += y[i] * y[i]\n",
     " \n",
     "coeff = np.sqrt(y_sum/x_sum)\n",
     "\n",
     "coeff"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Out Of Box"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 488,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "array([2.50991471])"
       ]
      },
      "execution_count": 488,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "from sklearn.linear_model import LinearRegression\n",
     "\n",
     "lin_reg = LinearRegression()\n",
     "lin_reg.fit(X.reshape(-1,1),y)\n",
     "lin_reg.coef_"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Custom With Matrix"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 489,
    "metadata": {},
    "outputs": [],
    "source": [
     "X = X.reshape(-1,1)\n",
     "y = y.reshape(-1,1)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 490,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "(1000, 1)"
       ]
      },
      "execution_count": 490,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "X.shape"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 491,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "(1000, 1)"
       ]
      },
      "execution_count": 491,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "y.shape"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 492,
    "metadata": {},
    "outputs": [],
    "source": [
     "# @ in python is matrix multiplication which works the same way\n",
     "# as using np.dot()\n",
     "\n",
     "from sklearn.preprocessing import add_dummy_feature\n",
     "\n",
     "X_b = add_dummy_feature(X)\n",
     "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 493,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "array([[0.5989782 ],\n",
        "       [2.50991471]])"
       ]
      },
      "execution_count": 493,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "theta_best"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": ".venv",
    "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": "3.11.2"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }