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‎week0_05_Bias_Variance/README.md

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How to shoot yourself in your foot with preprocessing and cross-validation:
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[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/girafe-ai/ml-mipt/blob/basic_s21/week0_05_Bias_Variance/week0_05_Cross_validation_riddle.ipynb)
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Bias-variance decomposition visualization:
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[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/girafe-ai/ml-mipt/blob/basic_s21/week0_05_Bias_Variance/week0_05_BiasVariance.ipynb)

‎week0_05_Bias_Variance/week0_05_BiasVariance.ipynb

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‎week0_05_Bias_Variance/week0_05_Cross_validation_riddle.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Credits: this notebook origin (shared under MIT license) belongs to [ML course at ICL](https://github.com/yandexdataschool/MLatImperial2020) held by Yandex School of Data Analysis. Special thanks to the course team for making it available online.*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "Ij_zY4soDF2Z"
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},
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"source": [
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"## week0_05: Cross-validation riddle"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "qUCsY5OlDJPl"
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},
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"source": [
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"Here's a small example of cross-validation done wrongly. Can you spot the problem?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"colab": {},
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"colab_type": "code",
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"id": "mSUzkXsC-R4H"
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},
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"outputs": [],
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"source": [
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"# Some imports...\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from sklearn.svm import LinearSVC\n",
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"from sklearn.model_selection import KFold, cross_val_score\n",
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"from sklearn.metrics import accuracy_score"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "ZyDp3Xc_DaDM"
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},
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"source": [
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"**Plan:**\n",
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"\n",
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"- Let's create a binary classification dataset where targets are completely independent from the features\n",
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" - *(i.e. no model could ever predict them well)*\n",
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"- We'll do some simple feature selection\n",
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"- And cross-validate a model on this data\n",
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"\n",
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"**Q:** what accuracy do we expect (classes are even)?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "IHx51DKP8Rcf"
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},
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"source": [
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"We'll start from writing a class to select the best features:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"colab": {},
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"colab_type": "code",
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"id": "rRNmKZJJ8W7x"
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},
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"outputs": [],
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"source": [
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"class FeatureSelector:\n",
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" def __init__(self, num_features):\n",
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" self.n = num_features # number of best features to select\n",
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"\n",
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" def fit(self, X, y):\n",
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" # Select features that describe the targets best, i.e. have\n",
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" # highest correlation with them:\n",
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" covariance = ((X - X.mean(axis=0)) * (y[:,np.newaxis] - y.mean())).mean(axis=0)\n",
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" self.best_feature_ids = np.argsort(np.abs(covariance))[-self.n:]\n",
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"\n",
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" def transform(self, X):\n",
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" return X[:,self.best_feature_ids]\n",
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"\n",
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" def fit_transform(self, X, y):\n",
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" self.fit(X, y)\n",
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" return self.transform(X)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 34
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},
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"colab_type": "code",
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"id": "6mu9gHgNBk_V",
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"outputId": "020bdc20-04e3-45c3-a3a7-a4c2cf9139e5"
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CV score is 0.8741414141414141\n"
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]
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}
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],
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"source": [
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"num_features_total = 1000\n",
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"num_features_best = 100\n",
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"\n",
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"N = 100\n",
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"\n",
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"# Dataset generation\n",
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"X = np.random.normal(size=(N, num_features_total))\n",
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"y = np.random.randint(2, size=N)\n",
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"\n",
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"# Feature selection:\n",
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"X_best = FeatureSelector(num_features_best).fit_transform(X, y)\n",
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"\n",
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"# Simple classification model\n",
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"model = LinearSVC()\n",
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"\n",
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"# Estimatin accuracy using cross-validation:\n",
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"cv_score = cross_val_score(model, X_best, y, scoring='accuracy', cv=10, n_jobs=-1).mean()\n",
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"print(f\"CV score is {cv_score}\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "afadN3ZVFKjF"
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},
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"source": [
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"What's going on?! Why accuracy is so high?\n",
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"\n",
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"Maybe it just happened by chance? Let's repeat this experiment many times and histogram the results:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 265
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},
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"colab_type": "code",
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"id": "QDbOMXnuC6uw",
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"outputId": "597d41e7-482b-4f6a-8565-316644c1b04e"
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},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"num_features_total = 1000\n",
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"num_features_best = 100\n",
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"\n",
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"N = 100\n",
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"def experiment():\n",
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" # Dataset generation\n",
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" X = np.random.normal(size=(N, num_features_total))\n",
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" y = np.random.randint(2, size=N)\n",
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"\n",
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" # Feature selection:\n",
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" X_best = FeatureSelector(num_features_best).fit_transform(X, y)\n",
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"\n",
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" # Simple classification model\n",
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" model = LinearSVC()\n",
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"\n",
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" # Estimatin accuracy using cross-validation:\n",
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" return cross_val_score(model, X_best, y, scoring='accuracy', cv=10, n_jobs=-1).mean()\n",
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"\n",
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"results = [experiment() for _ in range(100)]\n",
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"plt.hist(results, bins=10);"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "8bLaEypoF5pb"
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},
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"source": [
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"Can you explain and fix this?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# It's dangerous to go alone. Take this!\n",
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"from sklearn.pipeline import Pipeline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# YOUR BEAUTIFUL FIX HERE"
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]
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}
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],
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"metadata": {
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"colab": {
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"include_colab_link": true,
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"name": "Cross-validation riddle.ipynb",
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"provenance": []
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},
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"kernelspec": {
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"display_name": "Py3 research env",
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"language": "python",
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"name": "py3_research"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}

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