code/day48 training models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a1bd062c",
   "metadata": {},
   "source": [
    "# Training models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c0c39b1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets generate some linear looking data to test linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3c21730a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(42)  \n",
    "m = 100             # number of instances\n",
    "X = 2*np.random.rand(m,1)  #column vector\n",
    "y= 4 + 3*X + np.random.rand(m,1) #column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a1855c1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import add_dummy_feature\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   #@ perform np.matmul()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7d104b78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.51359766],\n",
       "       [2.98323418]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "293ba8b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.51359766],\n",
       "       [10.48006601]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0],[2]])\n",
    "X_new_b = add_dummy_feature(X_new)\n",
    "y_predict = X_new_b @ theta_best         # matrix multipication\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0338f7ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9f520a9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.51359766],\n",
       "       [10.48006601]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# performing linear regression using scikit-learn straightforward\n",
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_,lin_reg.coef_\n",
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "501e5ff9",
   "metadata": {},
   "source": [
    "# Gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "834517bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1 # learning rate\n",
    "n_epochs = 1000\n",
    "m = len(X_b) # number of instances\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1) # randomly initialized model parameters\n",
    "for epoch in range(n_epochs):\n",
    " gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    " theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01916c77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.51359766],\n",
       "       [2.98323418]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07ab68e9",
   "metadata": {},
   "source": [
    "# Stochastic Gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "30747eaf",
   "metadata": {},
   "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",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "99ac06b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.51548062],\n",
       "       [2.9775157 ]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d815ee",
   "metadata": {},
   "source": [
    "### Using stochastic gd in linear regression using SGDRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2588fbe4",
   "metadata": {},
   "outputs": [
    {
     "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>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>"
      ],
      "text/plain": [
       "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6c888c51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.50316965]), array([2.99156535]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_\n"
   ]
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}