Training Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# The Normal Equation"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(42) # to make this code example reproducible\n",
    "m = 100 # number of instances\n",
    "X = 2 * np.random.rand(m, 1) # column vector\n",
    "y = 4 + 3 * X + np.random.randn(m, 1) # column vector\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis()\n",
    "plt.grid()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import add_dummy_feature\n",
    "\n",
    "X_b = add_dummy_feature(X) # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [2.77011339]])"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [9.75532293]])"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = add_dummy_feature(X_new) # add x0 = 1 to each isinstance\n",
    "y_predict = X_new_b @ theta_best\n",
    "y_predict"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.legend()\n",
    "plt.axis()\n",
    "plt.grid()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([4.21509616]), array([[2.77011339]]))"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [9.75532293]])"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [2.77011339]])"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [2.77011339]])"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b) @ y"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Batch Gradient Descent"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [],
   "source": [
    "eta = 0.1 # learning rate\n",
    "n_epochs = 1000\n",
    "m = len(X_b) # number of instances\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1) # randomly initialized model parameters\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "    theta = theta - eta * gradients"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21509616],\n       [2.77011339]])"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Stochastic Gradient Descent"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50 # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1) # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for iteration in range(m):\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index : random_index + 1]\n",
    "        yi = y[random_index : random_index + 1]\n",
    "        gradients = 2 * xi.T @ (xi @ theta - yi) # for SGD do not divide by m\n",
    "        eta = learning_schedule(epoch * m + iteration)\n",
    "        theta = theta - eta * gradients"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.21076011],\n       [2.74856079]])"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)",
      "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>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</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\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre></div></div></div></div></div>"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-5, penalty=None, eta0=0.01,\n",
    "                       n_iter_no_change=100, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel()) # y..ravel() because fit() expects 1D targets"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([4.21278812]), array([2.77270267]))"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Polynomial Regression"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.legend()\n",
    "plt.axis()\n",
    "plt.grid()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-0.75275929])"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0]"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-0.75275929,  0.56664654])"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_poly, y, \"b.\")\n",
    "plt.axis()\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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