Project 3 - Linear Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "860848ec",
   "metadata": {},
   "source": [
    "# Theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "331468bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.rand(100, 1)\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "67c31e46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.51359766],\n       [2.98323418]])"
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]   # add x0 = 1 to each instance\n",
    "\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T.dot(y))\n",
    "theta_best\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "9a5ae406",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 4.51359766],\n       [10.48006601]])"
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]\n",
    "\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "261787de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", label = \"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.legend(loc = \"upper left\" )\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "3a4e39c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(array([4.51359766]), array([[2.98323418]]))"
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sckit-learn's equivalent code\n",
    "\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "dc66f1af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 4.51359766],\n       [10.48006601]])"
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "77757c1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.51359766],\n       [2.98323418]])"
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Batch Gradient Descent\n",
    "eta = 0.1   # learnign rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "\n",
    "theta = np.random.rand(2, 1)    # random initialization\n",
    "\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2 / m * X_b.T.dot(X_b.dot(theta) - y)   # Gradient Descent Algorithm\n",
    "    theta = theta - eta * gradients\n",
    "    \n",
    "theta\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "6aaacd03",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Stochastic Gradient Descent (Using simulated annealing)\n",
    "m = 100\n",
    "\n",
    "n_epochs = 50\n",
    "t0, t1 = 5, 50   # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "\n",
    "theta = np.random.rand(2, 1)    # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i 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.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "    #print(theta)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "d08f286d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4.52035641],\n       [2.98600484]])"
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "2ea0509c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "SGDRegressor(eta0=0.1, max_iter=50, penalty=None)",
      "text/html": "<style>#sk-container-id-6 {color: black;background-color: white;}#sk-container-id-6 pre{padding: 0;}#sk-container-id-6 div.sk-toggleable {background-color: white;}#sk-container-id-6 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-6 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-6 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-6 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-6 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 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-6 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-6 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-6 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 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-6 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-6 div.sk-item {position: relative;z-index: 1;}#sk-container-id-6 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-6 div.sk-item::before, #sk-container-id-6 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-6 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-6 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-6 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-6 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-6 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-6 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-6 div.sk-label-container {text-align: center;}#sk-container-id-6 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-6 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(eta0=0.1, max_iter=50, penalty=None)</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-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(eta0=0.1, max_iter=50, penalty=None)</pre></div></div></div></div></div>"
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_regressor = SGDRegressor(max_iter = 50, penalty = None, eta0 = 0.1)\n",
    "sgd_regressor.fit(X, y.ravel())\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "f0d3d6c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(array([4.50306422]), array([3.00667898]))"
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_regressor.intercept_, sgd_regressor.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7ea6cd17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial Regression\n",
    "\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.rand(m, 1)\n",
    "\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "4e14cc3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(array([2.99335567]), array([2.99335567, 8.96017818]))"
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "poly_features = PolynomialFeatures(degree = 2, include_bias = False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0], X_poly[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "b821dff2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(array([2.44744008]), array([[1.02612412, 0.50812125]]))"
     },
     "execution_count": 103,
     "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": 104,
   "id": "46a19506",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.fit_transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "151afcae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Learning Curves\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2)\n",
    "    train_errors, val_errors = [], []\n",
    "\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))\n",
    "        val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
    "    plt.plot(np.sqrt(train_errors), \"r+-\", label = \"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", label = \"val\")\n",
    "    plt.axis([0, 80, 0, 2])\n",
    "    plt.legend(loc = \"upper left\")\n",
    "    plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "98ee2570",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_learning_curves(lin_reg, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "1d4781d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "polynomial_regression = make_pipeline(PolynomialFeatures(degree=10, include_bias=False), LinearRegression())\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "22a0e4b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "array([[2.13576832]])"
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ridge Regression\n",
    "\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.rand(m, 1) / 1.5\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "outputs": [
    {
     "data": {
      "text/plain": "array([2.0793482])"
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_regressor = SGDRegressor(penalty=\"l2\")\n",
    "\n",
    "sgd_regressor.fit(X, y.ravel())\n",
    "sgd_regressor.predict([[1.5]])\n",
    "\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "outputs": [
    {
     "data": {
      "text/plain": "array([2.1126616])"
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lasso Regression\n",
    "\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.1)    # We can use SGDRegressor(penalty=\"l1\"). They are same.\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "outputs": [
    {
     "data": {
      "text/plain": "array([2.12177065])"
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Elastic Net\n",
    "# It is between Ridge and Lasso regressions\n",
    "# Mix ratio r = 0 means Ridge, r = 1 means Lasso\n",
    "\n",
    "from sklearn.linear_model import ElasticNet\n",
    "\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])\n",
    "\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "outputs": [
    {
     "data": {
      "text/plain": "(2.408570926293389, SGDRegressor(eta0=0.002, penalty=None, random_state=42), 0)"
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Early stopping\n",
    "\n",
    "from copy import deepcopy\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# Creating quadratic dataset and split it\n",
    "\n",
    "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.rand(m, 1)\n",
    "X_train, y_train = X[: m // 2], y[: m // 2, 0]\n",
    "X_valid, y_valid = X[m // 2 :], y[m // 2 : , 0]\n",
    "\n",
    "preprocessing = make_pipeline(PolynomialFeatures(degree=90, include_bias=False), StandardScaler())\n",
    "X_train_prep = preprocessing.fit_transform(X_train)\n",
    "X_valid_prep = preprocessing.transform(X_valid)\n",
    "\n",
    "\n",
    "sgd_regressor = SGDRegressor(penalty=None, eta0=0.002, random_state=42)\n",
    "n_epochs = 500\n",
    "best_valid_rmse = float(\"inf\")\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_regressor.fit(X_train_prep, y_train)\n",
    "    y_valid_predict = sgd_regressor.predict(X_valid_prep)\n",
    "    val_error = mean_squared_error(y_valid, y_valid_predict, squared=False)\n",
    "    if val_error < best_valid_rmse:\n",
    "        best_valid_rmse = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = deepcopy(sgd_regressor)\n",
    "\n",
    "\n",
    "best_valid_rmse, best_model, best_epoch\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "outputs": [
    {
     "data": {
      "text/plain": "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])"
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "iris.keys()\n",
    "#iris[\"DESCR\"]"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 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 1 1 1 1 1 1 1 1 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2]\n"
     ]
    }
   ],
   "source": [
    "print(iris[\"target\"])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris[\"DESCR\"])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "outputs": [
    {
     "data": {
      "text/plain": "LogisticRegression()",
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     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][ : , 3: ]\n",
    "y = (iris[\"target\"] == 2)\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state = 42)\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "log_regression = LogisticRegression()\n",
    "log_regression.fit(X_train, y_train)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_regression.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[ : , 1] >= 0.5][0, 0]\n",
    "\n",
    "plt.plot(X_new, y_proba[ : , 1], \"g-\", label = \" Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[ : , 0], \"b--\", label = \"Not Iris-Virginica\")\n",
    "plt.plot([decision_boundary, decision_boundary], [0, 1], \"k:\", label=\"Decision Boundary\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "outputs": [
    {
     "data": {
      "text/plain": "1.6516516516516517"
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "outputs": [
    {
     "data": {
      "text/plain": "array([2])"
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][ : , (2, 3)]\n",
    "y = iris[\"target\"]\n",
    "\n",
    "\n",
    "softmax_regression  = LogisticRegression(multi_class = \"multinomial\", solver = \"lbfgs\", C = 10)\n",
    "softmax_regression.fit(X, y)\n",
    "softmax_regression.predict([[5, 2]])\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_regression.predict_proba([[5, 2]])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trying to visualize\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "custom_map = ListedColormap([\"#fafab0\", \"#9898ff\", \"#a0faa0\"])\n",
    "\n",
    "x0, x1 = np.meshgrid(np.linspace(0, 8, 500).reshape(-1, 1), np.linspace(0, 3.5, 200).reshape(-1, 1))\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = softmax_regression.predict_proba(X_new)\n",
    "y_predict = softmax_regression.predict(X_new)\n",
    "\n",
    "\n",
    "zz1 = y_proba[ : , 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "\n",
    "plt.plot(X[y == 2, 0], X[y == 2, 1], \"g^\", label = \"Iris-Virginica\")\n",
    "plt.plot(X[y == 1, 0], X[y == 1, 1], \"bs\", label = \"Iris-Versicolor\")\n",
    "plt.plot(X[y == 0, 0], X[y == 0, 1], \"yo\", label = \"Iris-Setosa\")\n",
    "\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap = custom_map)\n",
    "contour = plt.contour(x0, x1, zz, cmap = \"hot\")\n",
    "plt.clabel(contour, inline = 1)\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}