Nested cross-validation\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Why nested cross-validation?\n",
"\n",
"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.\n",
"\n",
"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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Nested cross-validation explained\n",
"\n",
"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.\n",
"\n",
"\n",
"\n",
"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:\n",
"\n",
"1. Divide the dataset into _K_ cross-validation folds at random.\n",
"2. For each fold _k=1,2,…,K_: (outer loop for evaluation of the model with selected hyperparameter) \n",
"\n",
" 2.1. Let `test` be fold _k_ \n",
" 2.2. Let `trainval` be all the data except those in fold _k_ \n",
" 2.3. Randomly split `trainval` into _L_ folds \n",
" 2.4. For each fold _l=1,2,…L_: (inner loop for hyperparameter tuning) \n",
"> 2.4.1 Let `val` be fold _l_ \n",
"> 2.4.2 Let `train` be all the data except those in `test` or `val` \n",
"> 2.4.3 Train each of _N_ models with each hyperparameter on `train`, and evaluate it on `val`. Keep track of the performance metrics \n",
"\n",
" 2.5. For each hyperparameter setting, calculate the average metrics score over the _L_ folds, and choose the best hyperparameter setting. \n",
" 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_ \n",
" \n",
"3. For each of _N_ models calculate the mean score over all _K_ folds, and report as the generalization error.\n",
"\n",
"In the picture above and the code below we chose _L = 2_ and _K = 5_, but you can choose different numbers.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Implementation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Load required packages\n",
"import numpy as np\n",
"from sklearn import datasets\n",
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.metrics import accuracy_score\n",
"from sklearn.model_selection import (GridSearchCV, StratifiedKFold,\n",
" cross_val_score, train_test_split)\n",
"from sklearn.neighbors import KNeighborsClassifier\n",
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.svm import SVC\n",
"from sklearn.tree import DecisionTreeClassifier"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Load the data\n",
"dataset = datasets.load_breast_cancer()\n",
"\n",
"# Create X from the features\n",
"X = dataset.data\n",
"\n",
"# Create y from the target\n",
"y = dataset.target"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Making train set for Nested CV and test set for final model evaluation\n",
"X_train, X_test, y_train, y_test = train_test_split(\n",
" X, y, train_size=0.8, test_size=0.2, random_state=1, stratify=y\n",
")\n",
"\n",
"# Initializing Classifiers\n",
"clf1 = LogisticRegression(solver=\"liblinear\", random_state=1)\n",
"clf2 = KNeighborsClassifier()\n",
"clf3 = DecisionTreeClassifier(random_state=1)\n",
"clf4 = SVC(kernel=\"rbf\", random_state=1)\n",
"\n",
"# Building the pipelines\n",
"pipe1 = Pipeline([(\"std\", StandardScaler()), (\"clf1\", clf1)])\n",
"\n",
"pipe2 = Pipeline([(\"std\", StandardScaler()), (\"clf2\", clf2)])\n",
"\n",
"pipe4 = Pipeline([(\"std\", StandardScaler()), (\"clf4\", clf4)])\n",
"\n",
"\n",
"# Setting up the parameter grids\n",
"param_grid1 = [\n",
" {\"clf1__penalty\": [\"l1\", \"l2\"], \"clf1__C\": np.power(10.0, np.arange(-4, 4))}\n",
"]\n",
"\n",
"param_grid2 = [{\"clf2__n_neighbors\": list(range(1, 10)), \"clf2__p\": [1, 2]}]\n",
"\n",
"param_grid3 = [\n",
" {\"max_depth\": list(range(1, 10)) + [None], \"criterion\": [\"gini\", \"entropy\"]}\n",
"]\n",
"\n",
"param_grid4 = [\n",
" {\n",
" \"clf4__C\": np.power(10.0, np.arange(-4, 4)),\n",
" \"clf4__gamma\": np.power(10.0, np.arange(-5, 0)),\n",
" }\n",
"]\n",
"\n",
"# Setting up multiple GridSearchCV objects as inner CV, 1 for each algorithm\n",
"gridcvs = {}\n",
"inner_cv = StratifiedKFold(n_splits=2, shuffle=True, random_state=1)\n",
"\n",
"for pgrid, est, name in zip(\n",
" (param_grid1, param_grid2, param_grid3, param_grid4),\n",
" (pipe1, pipe2, clf3, pipe4),\n",
" (\"Logit\", \"KNN\", \"DTree\", \"SVM\"),\n",
"):\n",
" gcv = GridSearchCV(\n",
" estimator=est,\n",
" param_grid=pgrid,\n",
" scoring=\"accuracy\",\n",
" n_jobs=1,\n",
" cv=inner_cv,\n",
" verbose=0,\n",
" refit=True,\n",
" )\n",
" gridcvs[name] = gcv"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Making an outer CV\n",
"outer_cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=1)\n",
"\n",
"for name, gs_est in sorted(gridcvs.items()):\n",
" nested_score = cross_val_score(gs_est, X=X_train, y=y_train, cv=outer_cv, n_jobs=1)\n",
" print(\n",
" \"%s | outer ACC %.2f%% +/- %.2f\"\n",
" % (name, nested_score.mean() * 100, nested_score.std() * 100)\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Fitting a model to the whole training set using the \"best\" algorithm\n",
"best_algo = gridcvs[\"SVM\"]\n",
"\n",
"best_algo.fit(X_train, y_train)\n",
"train_acc = accuracy_score(y_true=y_train, y_pred=best_algo.predict(X_train))\n",
"test_acc = accuracy_score(y_true=y_test, y_pred=best_algo.predict(X_test))\n",
"\n",
"print(\"Accuracy %.2f%% (average over CV train folds)\" % (100 * best_algo.best_score_))\n",
"print(\"Best Parameters: %s\" % gridcvs[\"SVM\"].best_params_)\n",
"print(\"Training Accuracy: %.2f%%\" % (100 * train_acc))\n",
"print(\"Test Accuracy: %.2f%%\" % (100 * test_acc))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Conclusion\n",
"\n",
"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.\n",
"\n",
"Writing this tutorial we used the following sources:\n",
"1. [Sebastian Rashka's article](https://sebastianraschka.com/blog/2018/model-evaluation-selection-part4.html)\n",
"2. [And also his code from GitHub](https://github.com/rasbt/model-eval-article-supplementary/blob/master/code/nested_cv_code.ipynb.)\n",
"3. [Weina Jin's article](https://weina.me/nested-cross-validation/)"
]
}
],
"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": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}