11_modelling_with-cross_validation.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Selecting a model with Cross-Validation\n",
    "##### Fundamental question in machine learning : how do we select a model that predicts well?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets \n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:,2:]\n",
    "y = iris.target "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#train-test split \n",
    "from sklearn.model_selection import train_test_split \n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,stratify=y, random_state=7)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#instantiating two nearest-neighbour \n",
    "\n",
    "from sklearn.neighbors import KNeighborsClassifier \n",
    "\n",
    "knn3 = KNeighborsClassifier(n_neighbors=3)\n",
    "knn5 = KNeighborsClassifier(n_neighbors=5)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Now scoring both algorithms using `cross_val_score` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score \n",
    "\n",
    "knn3_scores = cross_val_score(knn3, X_train, y_train, cv=4)\n",
    "knn5_scores = cross_val_score(knn5, X_train, y_train, cv=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.96428571, 0.92857143, 0.89285714, 1.        ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn3_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.96428571, 0.96428571, 0.92857143, 1.        ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn5_scores"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Getting $Mean$ of both list "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of Knn_3:  0.9464285714285714\n",
      "Mean of Knn_5:  0.9642857142857143\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean of Knn_3: \",knn3_scores.mean())\n",
    "print(\"Mean of Knn_5: \",knn5_scores.mean())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Getting $Standard Deviation$ of both list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard Deviation of Knn_3:  0.039929785312496226\n",
      "Standard Deviation of Knn_5:  0.025253813613805257\n"
     ]
    }
   ],
   "source": [
    "print(\"Standard Deviation of Knn_3: \", knn3_scores.std())\n",
    "print(\"Standard Deviation of Knn_5: \", knn5_scores.std())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Knn_5 performed better and bit stable, therefore to be picked"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### K-Fold Cross Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Working on demo dataset \n",
    "\n",
    "import numpy as np \n",
    "X = np.array([[1,2],[3,4],[5,6],[7,8],[1,2],[3,4],[5,6],[7,8]])\n",
    "y = np.array([1,2,1,2,1,2,1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold \n",
    "kf = KFold(n_splits=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round:  1 Training Indices:  [2 3 4 5 6 7] Testing Indices:  [0 1]\n",
      "Round:  2 Training Indices:  [0 1 4 5 6 7] Testing Indices:  [2 3]\n",
      "Round:  3 Training Indices:  [0 1 2 3 6 7] Testing Indices:  [4 5]\n",
      "Round:  4 Training Indices:  [0 1 2 3 4 5] Testing Indices:  [6 7]\n"
     ]
    }
   ],
   "source": [
    "#now iterating through the generator \n",
    "\n",
    "cc = 1 \n",
    "for train_index, test_index in kf.split(X):\n",
    "    print(\"Round: \",cc, \"Training Indices: \",train_index, \"Testing Indices: \",test_index)\n",
    "    cc +=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kf.get_n_splits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2, 3, 4, 5]), array([6, 7]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To view the data in the folds themselves, store the generator as list \n",
    "indices_list = list(kf.split(X))\n",
    "indices_list[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6],\n",
       "       [7, 8],\n",
       "       [1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_indices, test_indices = indices_list[3]\n",
    "X[train_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 1, 2, 1, 2])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[train_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 6],\n",
       "       [7, 8]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[test_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[test_indices]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Balanced Cross-Validation\n",
    "##### Using `stratified cross-validation` this way different sets will have different values for the target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import StratifiedKFold \n",
    "skf = StratifiedKFold(n_splits=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round:  1 Training Indices:  [2 3 4 5 6 7] Testing Indices:  [0 1]\n",
      "Round:  2 Training Indices:  [0 1 4 5 6 7] Testing Indices:  [2 3]\n",
      "Round:  3 Training Indices:  [0 1 2 3 6 7] Testing Indices:  [4 5]\n",
      "Round:  4 Training Indices:  [0 1 2 3 4 5] Testing Indices:  [6 7]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "cc = 1 \n",
    "for train_index, test_index in skf.split(X,y):\n",
    "    print(\"Round: \",cc, \"Training Indices: \",train_index, \"Testing Indices: \",test_index)\n",
    "    cc +=1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### `stratefied K-Fold` takes two arguement $X$ and $y$. It tries to distribtue the target $y$ with the same distribution in each of the fold sets"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### `StratifiedShuffleSplit` reshuffle the stratified fold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import StratifiedShuffleSplit \n",
    "sss = StratifiedShuffleSplit(n_splits=5, test_size=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round:  1 Training Indices:  [0 3 4 2 5 1] Testing Indices:  [6 7]\n",
      "Round:  2 Training Indices:  [5 3 4 2 0 1] Testing Indices:  [7 6]\n",
      "Round:  3 Training Indices:  [4 5 6 1 0 7] Testing Indices:  [2 3]\n",
      "Round:  4 Training Indices:  [5 2 3 0 4 7] Testing Indices:  [6 1]\n",
      "Round:  5 Training Indices:  [3 5 7 6 4 2] Testing Indices:  [0 1]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "cc = 1 \n",
    "for train_index, test_index in sss.split(X,y):\n",
    "    print(\"Round: \",cc, \"Training Indices: \",train_index, \"Testing Indices: \",test_index)\n",
    "    cc +=1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Cross-Validation with ShuffleSplit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Dataset')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline \n",
    "\n",
    "true_mean = 1000 \n",
    "true_std = 10 \n",
    "N = 1000 \n",
    "dataset = np.random.normal(loc=true_mean, scale=true_std, size=N)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax.hist(dataset, color='k',alpha=.65, histtype='stepfilled',bins=50)\n",
    "ax.set_title(\"Histogram of Dataset\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Estimating the mean of half of the dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000.2102346526106"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "holdout_set = dataset[:500]\n",
    "fitting_set = dataset[500:]\n",
    "estimate = fitting_set[:500].mean()\n",
    "estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "999.9317680110954"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Mean of the whole dataset \n",
    "data_mean = dataset.mean()\n",
    "data_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2c0bc2d86d0>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualizing the behaviour of ShuffleSplit \n",
    "\n",
    "from sklearn.model_selection import ShuffleSplit \n",
    "shuffle_split = ShuffleSplit(n_splits=100, test_size=.5,random_state=0)\n",
    "\n",
    "mean_p = []\n",
    "estimate_closeness = []\n",
    "\n",
    "for train_index, not_used_index in shuffle_split.split(fitting_set):\n",
    "    mean_p.append(fitting_set[train_index].mean())\n",
    "    shuf_estimate = np.mean(mean_p)\n",
    "    estimate_closeness.append(np.abs(shuf_estimate - data_mean))\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(estimate_closeness)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.9.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}