#!/usr/bin/env python # coding: utf-8 #
# # # ## [mlcourse.ai](https://mlcourse.ai) – Open Machine Learning Course # ###
Author: Tatyana Kudasova, ODS Slack @kudasova # # ##
Tutorial # ##
Nested cross-validation # # ### Why nested cross-validation? # # Often we want to tune the parameters of a model. That is, we want to find the value of a parameter that minimizes our loss function. The best way to do this, as we already know, is cross-validation. # # However, as Cawley and Talbot pointed out in their [2010 paper](http://jmlr.org/papers/volume11/cawley10a/cawley10a.pdf), since we used the test set to both select the values of the parameter and evaluate the model, we risk optimistically biasing our model evaluations. For this reason, if a test set is used to select model parameters, then we need a different test set to get an unbiased evaluation of that selected model. Mainly, we can think of model selection as another training procedure, and hence, we would need a decently-sized, independent test set that we have not seen before to get an unbiased estimate of the models’ performance. Often, this is not affordable. A good way to overcome this problem is to use nested cross-validation. # ### Nested cross-validation explained # # The nested cross-validation has an inner cross-validation nested in an outer cross-validation. First, an inner cross-validation is used to tune the parameters and select the best model. Second, an outer cross-validation is used to evaluate the model selected by the inner cross-validation. # # # # Imagine that we have _N_ models and we want to use _L_-fold inner cross-validation to tune hyperparameters and K-fold outer cross validation to evaluate the models. Then the algorithm is as follows: # # 1. Divide the dataset into _K_ cross-validation folds at random. # 2. For each fold _k=1,2,…,K_: (outer loop for evaluation of the model with selected hyperparameter)
# # 2.1. Let `test` be fold _k_
# 2.2. Let `trainval` be all the data except those in fold _k_
# 2.3. Randomly split `trainval` into _L_ folds
# 2.4. For each fold _l=1,2,…L_: (inner loop for hyperparameter tuning)
# > 2.4.1 Let `val` be fold _l_
# > 2.4.2 Let `train` be all the data except those in `test` or `val`
# > 2.4.3 Train each of _N_ models with each hyperparameter on `train`, and evaluate it on `val`. Keep track of the performance metrics
# # 2.5. For each hyperparameter setting, calculate the average metrics score over the _L_ folds, and choose the best hyperparameter setting.
# 2.6. Train each of _N_ models with the best hyperparameter on `trainval`. Evaluate its performance on `test` and save the score for fold _k_
# # 3. For each of _N_ models calculate the mean score over all _K_ folds, and report as the generalization error. # # In the picture above and the code below we chose _L = 2_ and _K = 5_, but you can choose different numbers. # # ### Implementation # In: # Load required packages import numpy as np from sklearn import datasets from sklearn.model_selection import GridSearchCV from sklearn.model_selection import train_test_split from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import cross_val_score from sklearn.pipeline import Pipeline from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LogisticRegression from sklearn.neighbors import KNeighborsClassifier from sklearn.tree import DecisionTreeClassifier from sklearn.svm import SVC from sklearn.metrics import accuracy_score # The data for this tutorial is [breast cancer data](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_breast_cancer.html) with 30 features and a binary target variable. # In: # Load the data dataset = datasets.load_breast_cancer() # Create X from the features X = dataset.data # Create y from the target y = dataset.target # In: # Making train set for Nested CV and test set for final model evaluation X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.8, test_size=0.2, random_state=1, stratify=y) # Initializing Classifiers clf1 = LogisticRegression(solver='liblinear', random_state=1) clf2 = KNeighborsClassifier() clf3 = DecisionTreeClassifier(random_state=1) clf4 = SVC(kernel='rbf', random_state=1) # Building the pipelines pipe1 = Pipeline([('std', StandardScaler()), ('clf1', clf1)]) pipe2 = Pipeline([('std', StandardScaler()), ('clf2', clf2)]) pipe4 = Pipeline([('std', StandardScaler()), ('clf4', clf4)]) # Setting up the parameter grids param_grid1 = [{'clf1__penalty': ['l1', 'l2'], 'clf1__C': np.power(10., np.arange(-4, 4))}] param_grid2 = [{'clf2__n_neighbors': list(range(1, 10)), 'clf2__p': [1, 2]}] param_grid3 = [{'max_depth': list(range(1, 10)) + [None], 'criterion': ['gini', 'entropy']}] param_grid4 = [{'clf4__C': np.power(10., np.arange(-4, 4)), 'clf4__gamma': np.power(10., np.arange(-5, 0))}] # Setting up multiple GridSearchCV objects as inner CV, 1 for each algorithm gridcvs = {} inner_cv = StratifiedKFold(n_splits=2, shuffle=True, random_state=1) for pgrid, est, name in zip((param_grid1, param_grid2, param_grid3, param_grid4), (pipe1, pipe2, clf3, pipe4), ('Logit', 'KNN', 'DTree', 'SVM')): gcv = GridSearchCV(estimator=est, param_grid=pgrid, scoring='accuracy', n_jobs=1, cv=inner_cv, verbose=0, refit=True) gridcvs[name] = gcv # In: # Making an outer CV outer_cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=1) for name, gs_est in sorted(gridcvs.items()): nested_score = cross_val_score(gs_est, X=X_train, y=y_train, cv=outer_cv, n_jobs=1) print('%s | outer ACC %.2f%% +/- %.2f' % (name, nested_score.mean() * 100, nested_score.std() * 100)) # In: # Fitting a model to the whole training set using the "best" algorithm best_algo = gridcvs['SVM'] best_algo.fit(X_train, y_train) train_acc = accuracy_score(y_true=y_train, y_pred=best_algo.predict(X_train)) test_acc = accuracy_score(y_true=y_test, y_pred=best_algo.predict(X_test)) print('Accuracy %.2f%% (average over CV train folds)' % (100 * best_algo.best_score_)) print('Best Parameters: %s' % gridcvs['SVM'].best_params_) print('Training Accuracy: %.2f%%' % (100 * train_acc)) print('Test Accuracy: %.2f%%' % (100 * test_acc)) # ### Conclusion # # In this tutorial we learned how to use nested cross-validation for hyperparameter tuning and model evaluation. Hope it will help you in your Kaggle competitions or your ML projects. # # Writing this tutorial we used the following sources: # 1. [Sebastian Rashka's article](https://sebastianraschka.com/blog/2018/model-evaluation-selection-part4.html) # 2. [And also his code from GitHub](https://github.com/rasbt/model-eval-article-supplementary/blob/master/code/nested_cv_code.ipynb.) # 3. [Weina Jin's article](https://weina.me/nested-cross-validation/)