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Cross_Val_Score, Grid Search and ROC Curves.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Recitation 3: Cross_Val_Score, Grid Search, ROC and Precision Recall Curves\n",
"\n",
"Author: Sachin K Sunny (ssunny [at symbol] andrew.cmu.edu)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"import torchvision\n",
"import torchvision.transforms as transforms\n",
"\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"np.random.seed(0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data preparation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"train_dataset = torchvision.datasets.MNIST(root='data/',\n",
" train=True,\n",
" transform=transforms.ToTensor(),\n",
" download=True)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"train_images = np.array([image.numpy() for image, label in train_dataset])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"train_labels = np.array([label for image, label in train_dataset])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(60000, 1, 28, 28)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"train_images.shape"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([5, 0, 4, ..., 5, 6, 8])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"train_labels"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(60000, 1, 28, 28)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"train_images.shape"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x18dd36d8f28>"
]
},
"execution_count": 8,
"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.imshow(train_images[0][0], cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"train_images = train_images[:2000]\n",
"train_labels = train_labels[:2000]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"train_images_flat = train_images.reshape(len(train_images), -1) # flattens out each training image"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2000, 784)\n"
]
}
],
"source": [
"print(train_images_flat.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Choosing hyperparameter $k$ using cross_val_score"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"k: 1 cross validation accuracy: 0.8940314414702957\n",
"k: 2 cross validation accuracy: 0.8750245948993992\n",
"k: 4 cross validation accuracy: 0.8905486114357952\n",
"k: 8 cross validation accuracy: 0.8835135591526961\n",
"k: 16 cross validation accuracy: 0.8610167870864528\n",
"k: 32 cross validation accuracy: 0.8380138304232638\n",
"k: 64 cross validation accuracy: 0.7935141217579369\n",
"k: 128 cross validation accuracy: 0.7189772886960789\n",
"Best k: 1 cross validation accuracy: 0.8940314414702957\n"
]
}
],
"source": [
"from sklearn.model_selection import KFold\n",
"from sklearn.neighbors import KNeighborsClassifier\n",
"from sklearn.model_selection import cross_val_score\n",
"\n",
"highest_cross_val_accuracy = -np.inf\n",
"for k in 2**np.arange(0, 8):\n",
" classifier = KNeighborsClassifier(n_neighbors=k)\n",
" \n",
" scores = cross_val_score(classifier, train_images_flat, train_labels, scoring = 'accuracy', cv = 5)\n",
" \n",
" cross_val_accuracy = scores.mean()\n",
" print('k:', k, 'cross validation accuracy:', cross_val_accuracy)\n",
" \n",
" if cross_val_accuracy > highest_cross_val_accuracy:\n",
" highest_cross_val_accuracy = cross_val_accuracy\n",
" best_k = k\n",
"\n",
"print('Best k:', best_k, 'cross validation accuracy:', highest_cross_val_accuracy)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using Random Forest classifiers and Grid Search"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we see cross-validation for random forests. Importantly, now we sweep over two hyperparameters."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'max_features': 112, 'min_samples_leaf': 4}"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.ensemble import RandomForestClassifier\n",
"\n",
"from sklearn.model_selection import GridSearchCV\n",
"\n",
"num_features = train_images_flat.shape[1]\n",
"max_features= [int(np.ceil(np.sqrt(num_features) / 4)),int(np.ceil(np.sqrt(num_features))),\\\n",
" int(np.ceil(np.sqrt(num_features) * 4))]\n",
"min_samples_leaf = [1, 2, 4, 8, 16]\n",
"\n",
"params = {'max_features': max_features, 'min_samples_leaf': min_samples_leaf} #hyperparameters to loop over\n",
"\n",
"classifier = RandomForestClassifier()\n",
"\n",
"gridsearch = GridSearchCV(classifier, params, cv=5) #create the grid search object\n",
"\n",
"gridsearch.fit(train_images_flat, train_labels) #run the grid search for each hyperparemeter configuration\n",
"\n",
"#which configuration gave the best results?\n",
"gridsearch.cv_results_['params'][np.argmax(gridsearch.cv_results_['mean_test_score'])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ROC curve"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- [ROC curves](https://en.wikipedia.org/wiki/Receiver_operating_characteristic) are a way to evaluate classifiers\n",
"- There is an inherent tradeoff between true positives and false positives\n",
"\n",
"\n",
"More on the scikit-learn ROC curve module [here](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_curve.html)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"#Load Data \n",
"from sklearn import datasets\n",
"iris = datasets.load_iris()\n",
"Xi = iris.data\n",
"yi = iris.target\n",
"Xi, yi = Xi[yi != 2], yi[yi != 2]\n",
"n_samples, n_features = Xi.shape\n",
"\n",
"# Add noisy features\n",
"random_state = np.random.RandomState(0)\n",
"Xi = np.c_[Xi, random_state.randn(n_samples, 200 * n_features)] #concatenates new features\n",
"\n",
"#Hold Out Test Data\n",
"from sklearn.model_selection import train_test_split\n",
"Xi_train, Xi_test, yi_train, yi_test = train_test_split(Xi, yi, test_size=0.25, shuffle=True)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from sklearn.metrics import roc_curve\n",
"\n",
"# Random Forests\n",
"ntrees= [1, 10, 20, 100, 1000]\n",
"colors = [\"C0\", \"C1\", 'C2','C3', 'C4']\n",
"\n",
"plt.figure(figsize=(10,10))\n",
"for i in range(len(ntrees)):\n",
" clf_rf = RandomForestClassifier(n_estimators=ntrees[i])\n",
" clf_rf.fit(Xi_train, yi_train)\n",
" y_score = clf_rf.predict_proba(Xi_test)[:,1] #probabilistic classifier, so the model outputs probabilities\n",
" fpr, tpr, thresholds = roc_curve(yi_test, y_score, pos_label=1)\n",
" auc = np.trapz(tpr, fpr)\n",
" plt.plot(fpr, tpr, linestyle='-', alpha=0.5, color= colors[i], label = ntrees[i])\n",
"\n",
"plt.title(\"ROC curve\")\n",
"plt.legend(title = \"Number of trees\", loc = \"best\")\n",
"plt.xlabel(\"FPR\")\n",
"plt.ylabel(\"TPR\")\n",
"plt.grid()\n",
"plt.show() "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Predicting Diabetes Cases"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The National Institute of Diabetes and Digestive and Kidney Diseases has collected the Pima Indians dataset, which contains data from clinical exams for women age 21 and above of Pima Indian origins. In this problem, we predict whether each woman has diabetes or not based on diagnostic measurements.\n",
"\n",
"For each woman, the following features were recorded:\n",
"- Pregnancies: Number of times pregnant\n",
"- Glucose: Plasma glucose concentration a 2 hours in an oral glucose tolerance test\n",
"- Blood Pressure: Diastolic blood pressure (mm Hg)\n",
"- Skin Thickness: Triceps skin fold thickness (mm)\n",
"- Insulin: 2-Hour serum insulin (mu U/ml)\n",
"- BMI: Body mass index (weight in kg/(height in m)^2)\n",
"- Diabetes Pedigree Function: Diabetes pedigree function\n",
"- Age: Age (years)\n",
"\n",
"Per woman, the label is binary (1=diabetic, 0=not diabetic)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We begin by loading in the data:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(576, 8) (576,)\n",
"(192, 8) (192,)\n"
]
}
],
"source": [
"diabetes_X_train = np.loadtxt('diabetes_X_train.txt')\n",
"diabetes_y_train = np.loadtxt('diabetes_y_train.txt')\n",
"diabetes_X_test = np.loadtxt('diabetes_X_test.txt')\n",
"diabetes_y_test = np.loadtxt('diabetes_y_test.txt')\n",
"diabetes_features = ['Pregnancies',\n",
" 'Glucose',\n",
" 'Blood Pressure',\n",
" 'Skin Thickness',\n",
" 'Insulin',\n",
" 'BMI',\n",
" 'Diabetes Pedigree Function',\n",
" 'Age']\n",
"print(diabetes_X_train.shape, diabetes_y_train.shape)\n",
"print(diabetes_X_test.shape, diabetes_y_test.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Staring at Data\n",
"\n",
"Explore the training data by drawing a histogram for each feature."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"scrolled": false
},
"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"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"# ------------------------------------------------------------------------------\n",
"# TODO: WRITE YOUR CODE HERE\n",
"#\n",
"\n",
"for idx in range(diabetes_X_train.shape[1]):\n",
" plt.hist(diabetes_X_train[:, idx])\n",
" plt.xlabel(diabetes_features[idx])\n",
" plt.ylabel('Raw count')\n",
" plt.show()\n",
"\n",
"#\n",
"# END OF YOUR CODE\n",
"# ------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Question:\n",
"Clearly explain why the features should be standardized."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### SOLUTION - \n",
"The feature values have scales that are drastically different by orders of magnitude (for instance, compare insulin with diabetes pedigree function). Standardizing (by subtracting the mean and dividing by the standard deviation) would prevent the feature with the largest scale from dominating the analysis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Question: \n",
"Suppose that we are standardizing the data (by subtracting off each feature's mean and dividing by its standard deviation) and also doing cross-validation. Explain why standardization should *not* be applied to the full training dataset first before running cross-validation. When should standardization be run?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### SOLUTION - \n",
"Standardization should be applied within each cross-validation fold's training data and not across the full training dataset first. Each fold of cross-validation is meant to mimic what the actual setup is like during test time. In particular, if we were to standardize across the entire training dataset first, and then hide part of it to use as a validation set, we have contaminated our training data with validation data! Specifically, we have used each fold's validation data's values in standardizing features within the same fold's training data! Instead, within each cross-validation fold, we standardize based on that fold's training data's feature vectors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model Selection\n",
"We shall use 5-fold cross-validation but with a twist! For each fold, compute two different scores: precision and recall (separately and not the F1 score). Use a random forest classifier, sweeping over 4 different `n_estimators` values (50, 100, 150, 200) and 6 `max_depth` values (2, 3, 4, 5, 6, 7), i.e., sweep over a total of 4x6=24 hyperparameter settings. For the `RandomForestClassifier`, aside from `n_estimators` and `max_depth`, only specify one additional setting `random_state=95865`."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"num_trees: 50 max_depth: 2 Precision: 0.795 Recall: 0.381\n",
"num_trees: 50 max_depth: 3 Precision: 0.734 Recall: 0.439\n",
"num_trees: 50 max_depth: 4 Precision: 0.745 Recall: 0.490\n",
"num_trees: 50 max_depth: 5 Precision: 0.735 Recall: 0.541\n",
"num_trees: 50 max_depth: 6 Precision: 0.752 Recall: 0.555\n",
"num_trees: 50 max_depth: 7 Precision: 0.725 Recall: 0.567\n",
"num_trees: 100 max_depth: 2 Precision: 0.826 Recall: 0.393\n",
"num_trees: 100 max_depth: 3 Precision: 0.767 Recall: 0.446\n",
"num_trees: 100 max_depth: 4 Precision: 0.750 Recall: 0.476\n",
"num_trees: 100 max_depth: 5 Precision: 0.731 Recall: 0.525\n",
"num_trees: 100 max_depth: 6 Precision: 0.742 Recall: 0.539\n",
"num_trees: 100 max_depth: 7 Precision: 0.717 Recall: 0.545\n",
"num_trees: 150 max_depth: 2 Precision: 0.793 Recall: 0.357\n",
"num_trees: 150 max_depth: 3 Precision: 0.781 Recall: 0.446\n",
"num_trees: 150 max_depth: 4 Precision: 0.755 Recall: 0.481\n",
"num_trees: 150 max_depth: 5 Precision: 0.742 Recall: 0.529\n",
"num_trees: 150 max_depth: 6 Precision: 0.741 Recall: 0.539\n",
"num_trees: 150 max_depth: 7 Precision: 0.732 Recall: 0.546\n",
"num_trees: 200 max_depth: 2 Precision: 0.811 Recall: 0.383\n",
"num_trees: 200 max_depth: 3 Precision: 0.770 Recall: 0.432\n",
"num_trees: 200 max_depth: 4 Precision: 0.757 Recall: 0.485\n",
"num_trees: 200 max_depth: 5 Precision: 0.741 Recall: 0.519\n",
"num_trees: 200 max_depth: 6 Precision: 0.745 Recall: 0.548\n",
"num_trees: 200 max_depth: 7 Precision: 0.716 Recall: 0.555\n"
]
},
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Precision')"
]
},
"execution_count": 18,
"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": [
"from sklearn.preprocessing import StandardScaler\n",
"\n",
"# WARNING: YOU SHOULD ONLY HAVE TO WRITE CODE IN THE PART BELOW THAT SAYS \"TODO\"\n",
"kf = KFold(n_splits=5, random_state=95865, shuffle=True)\n",
"num_trees_choices = [50, 100, 150, 200]\n",
"max_depth_choices = [2, 3, 4, 5, 6, 7]\n",
"hyperparameter_choices = [(num_trees, max_depth)\n",
" for num_trees in num_trees_choices\n",
" for max_depth in max_depth_choices]\n",
"rf_cross_validation_precision_scores = []\n",
"rf_cross_validation_recall_scores = []\n",
"\n",
"for num_trees, max_depth in hyperparameter_choices:\n",
" # --------------------------------------------------------------------------\n",
" # TODO: WRITE YOUR CODE HERE\n",
" #\n",
" \n",
" \n",
" fold_precision_scores = []\n",
" fold_recall_scores = []\n",
" for train_indices, val_indices in kf.split(diabetes_X_train):\n",
" fold_X_train = diabetes_X_train[train_indices]\n",
" fold_y_train = diabetes_y_train[train_indices]\n",
" fold_X_val = diabetes_X_train[val_indices]\n",
" fold_y_val = diabetes_y_train[val_indices]\n",
" \n",
" fold_scaler = StandardScaler()\n",
" fold_X_train_standardized = fold_scaler.fit_transform(fold_X_train)\n",
" fold_classifier = RandomForestClassifier(n_estimators=num_trees, max_depth=max_depth, random_state=95865)\n",
" fold_classifier.fit(fold_X_train_standardized, fold_y_train)\n",
" fold_y_val_predicted = fold_classifier.predict(fold_scaler.transform(fold_X_val))\n",
" \n",
" fold_true_pred_mask = (fold_y_val_predicted == 1)\n",
" if fold_true_pred_mask.sum() > 0:\n",
" fold_precision = (fold_y_val[fold_true_pred_mask] == 1).mean()\n",
" else:\n",
" # corner case to avoid division by 0\n",
" fold_precision = 0.\n",
" \n",
" fold_recall_mask = (fold_y_val == 1)\n",
" if fold_recall_mask.sum() > 0:\n",
" fold_recall = (fold_y_val_predicted[fold_recall_mask] == 1).mean()\n",
" else:\n",
" # corner case to avoid division by 0\n",
" fold_recall = 0.\n",
" \n",
" fold_precision_scores.append(fold_precision)\n",
" fold_recall_scores.append(fold_recall)\n",
" cross_val_precision = np.mean(fold_precision_scores)\n",
" cross_val_recall = np.mean(fold_recall_scores)\n",
" \n",
" #\n",
" # END OF YOUR CODE\n",
" # --------------------------------------------------------------------------\n",
" \n",
" print('num_trees: %d' % num_trees,\n",
" 'max_depth: %d' % max_depth,\n",
" 'Precision: %5.3f' % cross_val_precision,\n",
" 'Recall: %5.3f' % cross_val_recall)\n",
" rf_cross_validation_precision_scores.append(cross_val_precision)\n",
" rf_cross_validation_recall_scores.append(cross_val_recall)\n",
"\n",
"plt.scatter(rf_cross_validation_recall_scores,\n",
" rf_cross_validation_precision_scores)\n",
"plt.xlabel('Recall')\n",
"plt.ylabel('Precision')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the precision-recall plot above, suppose that for our clinical application, we want at least a *true positive rate* of 60%. Under this constraint, what is the largest precision that we could approximately be able to achieve according to our cross validation results? Which value of hyperparameters (among the ones we tried in cross validation) does this roughly correspond to?\n",
"\n",
"**Solution**: Among the hyperparameter settings tested for random forests, none achieves recall of at least 60%. Thus, we cannot say what precision is possible beyond the trivial lower bound of 0%.\n",
"\n",
"**Important observation**: Your answer to the above question should make it clear that using training data and a precision-recall curve, we can actually pick a hyperparameter based on some application-specific constraint. The hyperparameter chosen can then be used for test data!"
]
}
],
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diabetes_X_train.txt
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