TrainingLinearModels.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07cd7794",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ccd9aa",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "## The Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65e00aee",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = 3 * np.random.rand(200, 1)\n",
    "y = -5 + 2 * X + np.random.randn(200, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8bb6bf16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52d7a1a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((200, 1)), X]\n",
    "best_theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5e5b5830",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4.88498178],\n",
       "       [ 1.87486332]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3c2106b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4.88498178],\n",
       "       [ 0.73960819]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [3]])\n",
    "X_new_b = np.c_[np.ones((2,1)), X_new]\n",
    "y_predict = X_new_b.dot(best_theta)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aeed3746",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, 'r-')\n",
    "plt.plot(X, y, '.b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c52e6cbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5b4e6259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c2ed2ac0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.88498178])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d3647309",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.87486332]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69abd287",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "\n",
    "## Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ca28f403",
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1 # learning rate\n",
    "max_iterations = 1000\n",
    "m = 200 # number of samples\n",
    "\n",
    "theta = np.random.randn(2,1) # random initialization\n",
    "\n",
    "for i in range(max_iterations):\n",
    "    gradient = 2 / m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "56ca3e49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4.88498178],\n",
       "       [ 1.87486332]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3135758",
   "metadata": {},
   "source": [
    "## Stochastic GD with learning schedule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "92ad374b",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_epoch = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b7349346",
   "metadata": {},
   "outputs": [],
   "source": [
    "def learning_schedule(t, t0=5, t1=50):\n",
    "    return t0 / (t + t1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bb270e71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\t0.09803921568627451\t0.09615384615384616\t0.09433962264150944\t0.09259259259259259\t0.09090909090909091\t0.08928571428571429\t0.08771929824561403\t0.08620689655172414\t0.0847457627118644\t0.08333333333333333\t0.08196721311475409\t0.08064516129032258\t0.07936507936507936\t0.078125\t0.07692307692307693\t0.07575757575757576\t0.07462686567164178\t0.07352941176470588\t0.07246376811594203\t0.07142857142857142\t0.07042253521126761\t0.06944444444444445\t0.0684931506849315\t0.06756756756756757\t0.06666666666666667\t0.06578947368421052\t0.06493506493506493\t0.0641025641025641\t0.06329113924050633\t0.0625\t0.06172839506172839\t0.06097560975609756\t0.060240963855421686\t0.05952380952380952\t0.058823529411764705\t0.05813953488372093\t0.05747126436781609\t0.056818181818181816\t0.056179775280898875\t0.05555555555555555\t0.054945054945054944\t0.05434782608695652\t0.053763440860215055\t0.05319148936170213\t0.05263157894736842\t0.052083333333333336\t0.05154639175257732\t0.05102040816326531\t0.050505050505050504\t\n"
     ]
    }
   ],
   "source": [
    "for i in range(n_epoch):\n",
    "    print(learning_schedule(i), end='\\t')\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c84ce12d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.21413066],\n",
       "       [-0.20474585]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.random.randn(2, 1)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "90d64179",
   "metadata": {},
   "outputs": [],
   "source": [
    "for epoch in range(n_epoch):\n",
    "    for i in range(m):\n",
    "        random_index = np.random.randint(m) # choosing an instance by random (uniform dist)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fd7e48bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4.88483162],\n",
       "       [ 1.86423982]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a3c798a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import SGDRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "02a18908",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(eta0=0.1, penalty=None)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "eee215cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-4.90079062]), array([1.83343292]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a309d94",
   "metadata": {},
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "94981bb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m,1) - 3\n",
    "y = 0.9 * X ** 2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b7439865",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, 'b*')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9281e71e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "513a7788",
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c91369a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.31153808]), array([-1.31153808,  1.72013214]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0], X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3267211a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2.1262766]), array([[0.97718639, 0.86968393]]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f98b6794",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lin_reg.predict(X_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "47e9ebd3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.34063071],\n",
       "       [ 4.08414885],\n",
       "       [ 9.73093314],\n",
       "       [ 2.77570631],\n",
       "       [ 3.30687468],\n",
       "       [ 5.53307783],\n",
       "       [ 5.09621069],\n",
       "       [ 1.97335493],\n",
       "       [12.19066361],\n",
       "       [ 2.8220253 ],\n",
       "       [ 8.3744715 ],\n",
       "       [ 6.08844358],\n",
       "       [ 3.75191403],\n",
       "       [ 4.10245928],\n",
       "       [12.31264798],\n",
       "       [ 2.25362575],\n",
       "       [ 1.86837542],\n",
       "       [ 9.51619975],\n",
       "       [10.40885979],\n",
       "       [ 3.93580006],\n",
       "       [ 2.67868083],\n",
       "       [ 2.46315238],\n",
       "       [ 3.28210628],\n",
       "       [ 5.73256353],\n",
       "       [ 2.36803426],\n",
       "       [ 6.71264895],\n",
       "       [ 4.82664285],\n",
       "       [ 3.37747902],\n",
       "       [ 1.91293325],\n",
       "       [ 3.96820478],\n",
       "       [ 4.68607947],\n",
       "       [ 5.91343301],\n",
       "       [ 2.66251852],\n",
       "       [ 5.98716309],\n",
       "       [ 2.33198089],\n",
       "       [ 2.95303477],\n",
       "       [ 1.88242673],\n",
       "       [ 6.95156276],\n",
       "       [ 5.80297253],\n",
       "       [ 1.90317146],\n",
       "       [ 1.88145699],\n",
       "       [ 1.9295941 ],\n",
       "       [ 2.51796183],\n",
       "       [ 3.25960086],\n",
       "       [11.15316199],\n",
       "       [ 5.27794515],\n",
       "       [ 5.18287201],\n",
       "       [ 5.40231088],\n",
       "       [ 1.8607641 ],\n",
       "       [ 2.42211066],\n",
       "       [ 1.85281125],\n",
       "       [ 5.85658225],\n",
       "       [ 1.86191346],\n",
       "       [ 2.39160085],\n",
       "       [ 1.8943053 ],\n",
       "       [ 6.94773695],\n",
       "       [ 2.09062624],\n",
       "       [ 5.149603  ],\n",
       "       [ 5.09735818],\n",
       "       [ 1.87973025],\n",
       "       [ 3.49454133],\n",
       "       [ 8.41599366],\n",
       "       [ 6.9758244 ],\n",
       "       [ 5.62063119],\n",
       "       [ 2.94618827],\n",
       "       [ 1.87733631],\n",
       "       [ 5.38581596],\n",
       "       [ 2.2755386 ],\n",
       "       [ 6.88050323],\n",
       "       [ 1.97412725],\n",
       "       [ 6.389682  ],\n",
       "       [ 6.79057226],\n",
       "       [ 9.01933036],\n",
       "       [ 4.31309189],\n",
       "       [ 2.14755064],\n",
       "       [ 5.79531846],\n",
       "       [ 7.69447999],\n",
       "       [ 2.70835583],\n",
       "       [ 3.27968519],\n",
       "       [ 2.8872947 ],\n",
       "       [ 3.46839503],\n",
       "       [ 1.85480605],\n",
       "       [ 1.92581508],\n",
       "       [ 9.66162411],\n",
       "       [10.94416652],\n",
       "       [ 1.86308977],\n",
       "       [ 5.35464633],\n",
       "       [ 6.83567861],\n",
       "       [ 3.0977817 ],\n",
       "       [ 2.02127139],\n",
       "       [ 6.67021051],\n",
       "       [ 9.08316844],\n",
       "       [ 1.90328518],\n",
       "       [ 2.70901745],\n",
       "       [ 3.2265288 ],\n",
       "       [ 3.56663784],\n",
       "       [ 5.66965485],\n",
       "       [ 7.30684849],\n",
       "       [ 6.06997494],\n",
       "       [ 3.18151599]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "eb28489c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, 'b*')\n",
    "plt.plot(X, y_pred.ravel(), 'r.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c199386c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f57fbb6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_learning_curve(model, X, y, test_size=0.2):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=test_size)\n",
    "    \n",
    "    train_err = []\n",
    "    val_err = []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_pred = model.predict(X_train[:m])\n",
    "        y_val_pred = model.predict(X_val)\n",
    "        train_err.append(mean_squared_error(y_train[:m], y_train_pred[:m]))\n",
    "        val_err.append(mean_squared_error(y_val, y_val_pred))\n",
    "    \n",
    "    plt.plot(np.sqrt(train_err), 'r-+', label='train')\n",
    "    plt.plot(np.sqrt(val_err), 'b-', label='val')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "876074d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curve(lin_reg, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6a2ecc13",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8a7aa015",
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_reg = Pipeline([\n",
    "    ('poly_features', PolynomialFeatures(degree=10, include_bias=False)),\n",
    "    ('lin_reg', LinearRegression()),\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "390a1928",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_learning_curve(poly_reg, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "05f5babb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "65db4735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.6075264]), array([0.71162466]))"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.intercept_, lasso_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "24363bf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.60445576]), array([0.39649069]))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_reg = Lasso(alpha=1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.intercept_, lasso_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d2730490",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.60059237]), array([0.]))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_reg = Lasso(alpha=5)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.intercept_, lasso_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e2aa7310",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import ElasticNet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "bb83aa16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.60757475]), array([0.71658651]))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.intercept_, elastic_net.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "beb14fb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.6075264]), array([0.71162466]))"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=1)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.intercept_, elastic_net.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "cdb2d140",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hpc/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 317.8777317275141, tolerance: 0.07895789546834239\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([4.60762146]), array([0.72138049]))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.intercept_, elastic_net.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "365eb917",
   "metadata": {},
   "source": [
    "## IRIS Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "548ddedb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f303d28a",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "e6541af5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f9f61766",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['sepal length (cm)',\n",
       " 'sepal width (cm)',\n",
       " 'petal length (cm)',\n",
       " 'petal width (cm)']"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "4456eee1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "74ca3c68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris['target_names']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "e7d3e4b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# selecting just the petal_width\n",
    "X = iris['data'][:, 3:]\n",
    "y = (iris['target'] == 2).astype(np.int32) # 1 if virginica, 0 o.w."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "dfd5c6ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "156259f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "cc624e4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_reg = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "4682e6a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "281de3de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.1, 2.5)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(X), np.max(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "7470f1fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "6fed92f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 2)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "18903dd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.99250016e-01, 7.49984089e-04],\n",
       "       [9.99240201e-01, 7.59799387e-04],\n",
       "       [9.99230257e-01, 7.69743043e-04],\n",
       "       [9.99220183e-01, 7.79816732e-04],\n",
       "       [9.99209978e-01, 7.90022153e-04],\n",
       "       [9.99199639e-01, 8.00361024e-04],\n",
       "       [9.99189165e-01, 8.10835088e-04],\n",
       "       [9.99178554e-01, 8.21446109e-04],\n",
       "       [9.99167804e-01, 8.32195877e-04],\n",
       "       [9.99156914e-01, 8.43086202e-04]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba[:10, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "8fe4d2d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0469032310>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_proba[:, 0], \"b--\", label='Not virginica')\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", label='Virginica')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b1ea8ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.45722097, 0.54277903],\n",
       "       [0.66709636, 0.33290364]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict_proba([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "dbb03433",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0], dtype=int32)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35b3dd8c",
   "metadata": {},
   "source": [
    "## Softmax regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "cb41658c",
   "metadata": {},
   "outputs": [],
   "source": [
    "softmax_reg = LogisticRegression(multi_class='multinomial', solver='lbfgs', C=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "1137fae6",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris['data'][:, (2, 3)]\n",
    "y = iris['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "b1796ad2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial')"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "0756ee55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "27be05a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "32e4ad2c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}