.. _model_selection_tut: ============================================================ Model selection: choosing estimators and their parameters ============================================================ Score, and cross-validated scores ================================== As we have seen, every estimator exposes a ``score`` method that can judge the quality of the fit (or the prediction) on new data. **Bigger is better**. :: >>> from sklearn import datasets, svm >>> digits = datasets.load_digits() >>> X_digits = digits.data >>> y_digits = digits.target >>> svc = svm.SVC(C=1, kernel='linear') >>> svc.fit(X_digits[:-100], y_digits[:-100]).score(X_digits[-100:], y_digits[-100:]) 0.97999999999999998 To get a better measure of prediction accuracy (which we can use as a proxy for goodness of fit of the model), we can successively split the data in *folds* that we use for training and testing:: >>> import numpy as np >>> X_folds = np.array_split(X_digits, 3) >>> y_folds = np.array_split(y_digits, 3) >>> scores = list() >>> for k in range(3): ... # We use 'list' to copy, in order to 'pop' later on ... X_train = list(X_folds) ... X_test = X_train.pop(k) ... X_train = np.concatenate(X_train) ... y_train = list(y_folds) ... y_test = y_train.pop(k) ... y_train = np.concatenate(y_train) ... scores.append(svc.fit(X_train, y_train).score(X_test, y_test)) >>> print(scores) [0.93489148580968284, 0.95659432387312182, 0.93989983305509184] .. currentmodule:: sklearn.cross_validation This is called a :class:`KFold` cross validation .. _cv_generators_tut: Cross-validation generators ============================= The code above to split data in train and test sets is tedious to write. Scikit-learn exposes cross-validation generators to generate list of indices for this purpose:: >>> from sklearn import cross_validation >>> k_fold = cross_validation.KFold(n=6, n_folds=3) >>> for train_indices, test_indices in k_fold: ... print('Train: %s | test: %s' % (train_indices, test_indices)) Train: [2 3 4 5] | test: [0 1] Train: [0 1 4 5] | test: [2 3] Train: [0 1 2 3] | test: [4 5] The cross-validation can then be implemented easily:: >>> kfold = cross_validation.KFold(len(X_digits), n_folds=3) >>> [svc.fit(X_digits[train], y_digits[train]).score(X_digits[test], y_digits[test]) ... for train, test in kfold] [0.93489148580968284, 0.95659432387312182, 0.93989983305509184] To compute the ``score`` method of an estimator, the sklearn exposes a helper function:: >>> cross_validation.cross_val_score(svc, X_digits, y_digits, cv=kfold, n_jobs=-1) array([ 0.93489149, 0.95659432, 0.93989983]) `n_jobs=-1` means that the computation will be dispatched on all the CPUs of the computer. **Cross-validation generators** .. list-table:: * - :class:`KFold` **(n, k)** - :class:`StratifiedKFold` **(y, k)** - :class:`LeaveOneOut` **(n)** - :class:`LeaveOneLabelOut` **(labels)** * - Split it K folds, train on K-1 and then test on left-out - It preserves the class ratios / label distribution within each fold. - Leave one observation out - Takes a label array to group observations .. currentmodule:: sklearn.svm .. topic:: **Exercise** :class: green .. image:: ../../auto_examples/exercises/images/plot_cv_digits_001.png :target: ../../auto_examples/exercises/plot_cv_digits.html :align: right :scale: 90 On the digits dataset, plot the cross-validation score of a :class:`SVC` estimator with an linear kernel as a function of parameter ``C`` (use a logarithmic grid of points, from 1 to 10). .. literalinclude:: ../../auto_examples/exercises/plot_cv_digits.py :lines: 13-23 **Solution:** :ref:`example_exercises_plot_cv_digits.py` Grid-search and cross-validated estimators ============================================ Grid-search ------------- .. currentmodule:: sklearn.grid_search The sklearn provides an object that, given data, computes the score during the fit of an estimator on a parameter grid and chooses the parameters to maximize the cross-validation score. This object takes an estimator during the construction and exposes an estimator API:: >>> from sklearn.grid_search import GridSearchCV >>> gammas = np.logspace(-6, -1, 10) >>> clf = GridSearchCV(estimator=svc, param_grid=dict(gamma=gammas), ... n_jobs=-1) >>> clf.fit(X_digits[:1000], y_digits[:1000]) # doctest: +ELLIPSIS GridSearchCV(cv=None,... >>> clf.best_score_ # doctest: +ELLIPSIS 0.924... >>> clf.best_estimator_.gamma == 1e-6 True >>> # Prediction performance on test set is not as good as on train set >>> clf.score(X_digits[1000:], y_digits[1000:]) 0.94228356336260977 By default, the :class:`GridSearchCV` uses a 3-fold cross-validation. However, if it detects that a classifier is passed, rather than a regressor, it uses a stratified 3-fold. .. topic:: Nested cross-validation :: >>> cross_validation.cross_val_score(clf, X_digits, y_digits) ... # doctest: +ELLIPSIS array([ 0.935..., 0.958..., 0.937...]) Two cross-validation loops are performed in parallel: one by the :class:`GridSearchCV` estimator to set ``gamma`` and the other one by ``cross_val_score`` to measure the prediction performance of the estimator. The resulting scores are unbiased estimates of the prediction score on new data. .. warning:: You cannot nest objects with parallel computing (``n_jobs`` different than 1). .. _cv_estimators_tut: Cross-validated estimators ---------------------------- Cross-validation to set a parameter can be done more efficiently on an algorithm-by-algorithm basis. This is why for certain estimators the sklearn exposes :ref:`cross_validation` estimators that set their parameter automatically by cross-validation:: >>> from sklearn import linear_model, datasets >>> lasso = linear_model.LassoCV() >>> diabetes = datasets.load_diabetes() >>> X_diabetes = diabetes.data >>> y_diabetes = diabetes.target >>> lasso.fit(X_diabetes, y_diabetes) LassoCV(alphas=None, copy_X=True, cv=None, eps=0.001, fit_intercept=True, max_iter=1000, n_alphas=100, n_jobs=1, normalize=False, positive=False, precompute='auto', tol=0.0001, verbose=False) >>> # The estimator chose automatically its lambda: >>> lasso.alpha_ # doctest: +ELLIPSIS 0.01229... These estimators are called similarly to their counterparts, with 'CV' appended to their name. .. topic:: **Exercise** :class: green On the diabetes dataset, find the optimal regularization parameter alpha. **Bonus**: How much can you trust the selection of alpha? .. literalinclude:: ../../auto_examples/exercises/plot_cv_diabetes.py :lines: 17-24 **Solution:** :ref:`example_exercises_plot_cv_diabetes.py`