""" The :mod:`sklearn.model_selection._validation` module includes classes and functions to validate the model. """ # Author: Alexandre Gramfort , # Gael Varoquaux , # Olivier Grisel # License: BSD 3 clause from __future__ import print_function from __future__ import division import warnings import numbers import time import numpy as np import scipy.sparse as sp from ..base import is_classifier, clone from ..utils import indexable, check_random_state, safe_indexing from ..utils.fixes import astype from ..utils.validation import _is_arraylike, _num_samples from ..utils.metaestimators import _safe_split from ..externals.joblib import Parallel, delayed, logger from ..metrics.scorer import check_scoring from ..exceptions import FitFailedWarning from ._split import check_cv __all__ = ['cross_val_score', 'cross_val_predict', 'permutation_test_score', 'learning_curve', 'validation_curve'] def cross_val_score(estimator, X, y=None, groups=None, scoring=None, cv=None, n_jobs=1, verbose=0, fit_params=None, pre_dispatch='2*n_jobs'): """Evaluate a score by cross-validation Read more in the :ref:`User Guide `. Parameters ---------- estimator : estimator object implementing 'fit' The object to use to fit the data. X : array-like The data to fit. Can be, for example a list, or an array at least 2d. y : array-like, optional, default: None The target variable to try to predict in the case of supervised learning. groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set. scoring : string, callable or None, optional, default: None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. n_jobs : integer, optional The number of CPUs to use to do the computation. -1 means 'all CPUs'. verbose : integer, optional The verbosity level. fit_params : dict, optional Parameters to pass to the fit method of the estimator. pre_dispatch : int, or string, optional Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be: - None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs - An int, giving the exact number of total jobs that are spawned - A string, giving an expression as a function of n_jobs, as in '2*n_jobs' Returns ------- scores : array of float, shape=(len(list(cv)),) Array of scores of the estimator for each run of the cross validation. Examples -------- >>> from sklearn import datasets, linear_model >>> from sklearn.model_selection import cross_val_score >>> diabetes = datasets.load_diabetes() >>> X = diabetes.data[:150] >>> y = diabetes.target[:150] >>> lasso = linear_model.Lasso() >>> print(cross_val_score(lasso, X, y)) # doctest: +ELLIPSIS [ 0.33150734 0.08022311 0.03531764] See Also --------- :func:`sklearn.metrics.make_scorer`: Make a scorer from a performance metric or loss function. """ X, y, groups = indexable(X, y, groups) cv = check_cv(cv, y, classifier=is_classifier(estimator)) scorer = check_scoring(estimator, scoring=scoring) # We clone the estimator to make sure that all the folds are # independent, and that it is pickle-able. parallel = Parallel(n_jobs=n_jobs, verbose=verbose, pre_dispatch=pre_dispatch) scores = parallel(delayed(_fit_and_score)(clone(estimator), X, y, scorer, train, test, verbose, None, fit_params) for train, test in cv.split(X, y, groups)) return np.array(scores)[:, 0] def _fit_and_score(estimator, X, y, scorer, train, test, verbose, parameters, fit_params, return_train_score=False, return_parameters=False, return_n_test_samples=False, return_times=False, error_score='raise'): """Fit estimator and compute scores for a given dataset split. Parameters ---------- estimator : estimator object implementing 'fit' The object to use to fit the data. X : array-like of shape at least 2D The data to fit. y : array-like, optional, default: None The target variable to try to predict in the case of supervised learning. scorer : callable A scorer callable object / function with signature ``scorer(estimator, X, y)``. train : array-like, shape (n_train_samples,) Indices of training samples. test : array-like, shape (n_test_samples,) Indices of test samples. verbose : integer The verbosity level. error_score : 'raise' (default) or numeric Value to assign to the score if an error occurs in estimator fitting. If set to 'raise', the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error. parameters : dict or None Parameters to be set on the estimator. fit_params : dict or None Parameters that will be passed to ``estimator.fit``. return_train_score : boolean, optional, default: False Compute and return score on training set. return_parameters : boolean, optional, default: False Return parameters that has been used for the estimator. Returns ------- train_score : float, optional Score on training set, returned only if `return_train_score` is `True`. test_score : float Score on test set. n_test_samples : int Number of test samples. fit_time : float Time spent for fitting in seconds. score_time : float Time spent for scoring in seconds. parameters : dict or None, optional The parameters that have been evaluated. """ if verbose > 1: if parameters is None: msg = '' else: msg = '%s' % (', '.join('%s=%s' % (k, v) for k, v in parameters.items())) print("[CV] %s %s" % (msg, (64 - len(msg)) * '.')) # Adjust length of sample weights fit_params = fit_params if fit_params is not None else {} fit_params = dict([(k, _index_param_value(X, v, train)) for k, v in fit_params.items()]) if parameters is not None: estimator.set_params(**parameters) start_time = time.time() X_train, y_train = _safe_split(estimator, X, y, train) X_test, y_test = _safe_split(estimator, X, y, test, train) try: if y_train is None: estimator.fit(X_train, **fit_params) else: estimator.fit(X_train, y_train, **fit_params) except Exception as e: # Note fit time as time until error fit_time = time.time() - start_time score_time = 0.0 if error_score == 'raise': raise elif isinstance(error_score, numbers.Number): test_score = error_score if return_train_score: train_score = error_score warnings.warn("Classifier fit failed. The score on this train-test" " partition for these parameters will be set to %f. " "Details: \n%r" % (error_score, e), FitFailedWarning) else: raise ValueError("error_score must be the string 'raise' or a" " numeric value. (Hint: if using 'raise', please" " make sure that it has been spelled correctly.)") else: fit_time = time.time() - start_time test_score = _score(estimator, X_test, y_test, scorer) score_time = time.time() - start_time - fit_time if return_train_score: train_score = _score(estimator, X_train, y_train, scorer) if verbose > 2: msg += ", score=%f" % test_score if verbose > 1: end_msg = "%s -%s" % (msg, logger.short_format_time(score_time)) print("[CV] %s %s" % ((64 - len(end_msg)) * '.', end_msg)) ret = [train_score, test_score] if return_train_score else [test_score] if return_n_test_samples: ret.append(_num_samples(X_test)) if return_times: ret.extend([fit_time, score_time]) if return_parameters: ret.append(parameters) return ret def _score(estimator, X_test, y_test, scorer): """Compute the score of an estimator on a given test set.""" if y_test is None: score = scorer(estimator, X_test) else: score = scorer(estimator, X_test, y_test) if hasattr(score, 'item'): try: # e.g. unwrap memmapped scalars score = score.item() except ValueError: # non-scalar? pass if not isinstance(score, numbers.Number): raise ValueError("scoring must return a number, got %s (%s) instead." % (str(score), type(score))) return score def cross_val_predict(estimator, X, y=None, groups=None, cv=None, n_jobs=1, verbose=0, fit_params=None, pre_dispatch='2*n_jobs', method='predict'): """Generate cross-validated estimates for each input data point Read more in the :ref:`User Guide `. Parameters ---------- estimator : estimator object implementing 'fit' and 'predict' The object to use to fit the data. X : array-like The data to fit. Can be, for example a list, or an array at least 2d. y : array-like, optional, default: None The target variable to try to predict in the case of supervised learning. groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set. cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. n_jobs : integer, optional The number of CPUs to use to do the computation. -1 means 'all CPUs'. verbose : integer, optional The verbosity level. fit_params : dict, optional Parameters to pass to the fit method of the estimator. pre_dispatch : int, or string, optional Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be: - None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs - An int, giving the exact number of total jobs that are spawned - A string, giving an expression as a function of n_jobs, as in '2*n_jobs' method : string, optional, default: 'predict' Invokes the passed method name of the passed estimator. Returns ------- predictions : ndarray This is the result of calling ``method`` Examples -------- >>> from sklearn import datasets, linear_model >>> from sklearn.model_selection import cross_val_predict >>> diabetes = datasets.load_diabetes() >>> X = diabetes.data[:150] >>> y = diabetes.target[:150] >>> lasso = linear_model.Lasso() >>> y_pred = cross_val_predict(lasso, X, y) """ X, y, groups = indexable(X, y, groups) cv = check_cv(cv, y, classifier=is_classifier(estimator)) # Ensure the estimator has implemented the passed decision function if not callable(getattr(estimator, method)): raise AttributeError('{} not implemented in estimator' .format(method)) # We clone the estimator to make sure that all the folds are # independent, and that it is pickle-able. parallel = Parallel(n_jobs=n_jobs, verbose=verbose, pre_dispatch=pre_dispatch) prediction_blocks = parallel(delayed(_fit_and_predict)( clone(estimator), X, y, train, test, verbose, fit_params, method) for train, test in cv.split(X, y, groups)) # Concatenate the predictions predictions = [pred_block_i for pred_block_i, _ in prediction_blocks] test_indices = np.concatenate([indices_i for _, indices_i in prediction_blocks]) if not _check_is_permutation(test_indices, _num_samples(X)): raise ValueError('cross_val_predict only works for partitions') inv_test_indices = np.empty(len(test_indices), dtype=int) inv_test_indices[test_indices] = np.arange(len(test_indices)) # Check for sparse predictions if sp.issparse(predictions[0]): predictions = sp.vstack(predictions, format=predictions[0].format) else: predictions = np.concatenate(predictions) return predictions[inv_test_indices] def _fit_and_predict(estimator, X, y, train, test, verbose, fit_params, method): """Fit estimator and predict values for a given dataset split. Read more in the :ref:`User Guide `. Parameters ---------- estimator : estimator object implementing 'fit' and 'predict' The object to use to fit the data. X : array-like of shape at least 2D The data to fit. y : array-like, optional, default: None The target variable to try to predict in the case of supervised learning. train : array-like, shape (n_train_samples,) Indices of training samples. test : array-like, shape (n_test_samples,) Indices of test samples. verbose : integer The verbosity level. fit_params : dict or None Parameters that will be passed to ``estimator.fit``. method : string Invokes the passed method name of the passed estimator. Returns ------- predictions : sequence Result of calling 'estimator.method' test : array-like This is the value of the test parameter """ # Adjust length of sample weights fit_params = fit_params if fit_params is not None else {} fit_params = dict([(k, _index_param_value(X, v, train)) for k, v in fit_params.items()]) X_train, y_train = _safe_split(estimator, X, y, train) X_test, _ = _safe_split(estimator, X, y, test, train) if y_train is None: estimator.fit(X_train, **fit_params) else: estimator.fit(X_train, y_train, **fit_params) func = getattr(estimator, method) predictions = func(X_test) return predictions, test def _check_is_permutation(indices, n_samples): """Check whether indices is a reordering of the array np.arange(n_samples) Parameters ---------- indices : ndarray integer array to test n_samples : int number of expected elements Returns ------- is_partition : bool True iff sorted(indices) is np.arange(n) """ if len(indices) != n_samples: return False hit = np.zeros(n_samples, dtype=bool) hit[indices] = True if not np.all(hit): return False return True def _index_param_value(X, v, indices): """Private helper function for parameter value indexing.""" if not _is_arraylike(v) or _num_samples(v) != _num_samples(X): # pass through: skip indexing return v if sp.issparse(v): v = v.tocsr() return safe_indexing(v, indices) def permutation_test_score(estimator, X, y, groups=None, cv=None, n_permutations=100, n_jobs=1, random_state=0, verbose=0, scoring=None): """Evaluate the significance of a cross-validated score with permutations Read more in the :ref:`User Guide `. Parameters ---------- estimator : estimator object implementing 'fit' The object to use to fit the data. X : array-like of shape at least 2D The data to fit. y : array-like The target variable to try to predict in the case of supervised learning. groups : array-like, with shape (n_samples,), optional Labels to constrain permutation within groups, i.e. ``y`` values are permuted among samples with the same group identifier. When not specified, ``y`` values are permuted among all samples. When a grouped cross-validator is used, the group labels are also passed on to the ``split`` method of the cross-validator. The cross-validator uses them for grouping the samples while splitting the dataset into train/test set. scoring : string, callable or None, optional, default: None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. n_permutations : integer, optional Number of times to permute ``y``. n_jobs : integer, optional The number of CPUs to use to do the computation. -1 means 'all CPUs'. random_state : RandomState or an int seed (0 by default) A random number generator instance to define the state of the random permutations generator. verbose : integer, optional The verbosity level. Returns ------- score : float The true score without permuting targets. permutation_scores : array, shape (n_permutations,) The scores obtained for each permutations. pvalue : float The returned value equals p-value if `scoring` returns bigger numbers for better scores (e.g., accuracy_score). If `scoring` is rather a loss function (i.e. when lower is better such as with `mean_squared_error`) then this is actually the complement of the p-value: 1 - p-value. Notes ----- This function implements Test 1 in: Ojala and Garriga. Permutation Tests for Studying Classifier Performance. The Journal of Machine Learning Research (2010) vol. 11 """ X, y, groups = indexable(X, y, groups) cv = check_cv(cv, y, classifier=is_classifier(estimator)) scorer = check_scoring(estimator, scoring=scoring) random_state = check_random_state(random_state) # We clone the estimator to make sure that all the folds are # independent, and that it is pickle-able. score = _permutation_test_score(clone(estimator), X, y, groups, cv, scorer) permutation_scores = Parallel(n_jobs=n_jobs, verbose=verbose)( delayed(_permutation_test_score)( clone(estimator), X, _shuffle(y, groups, random_state), groups, cv, scorer) for _ in range(n_permutations)) permutation_scores = np.array(permutation_scores) pvalue = (np.sum(permutation_scores >= score) + 1.0) / (n_permutations + 1) return score, permutation_scores, pvalue permutation_test_score.__test__ = False # to avoid a pb with nosetests def _permutation_test_score(estimator, X, y, groups, cv, scorer): """Auxiliary function for permutation_test_score""" avg_score = [] for train, test in cv.split(X, y, groups): estimator.fit(X[train], y[train]) avg_score.append(scorer(estimator, X[test], y[test])) return np.mean(avg_score) def _shuffle(y, groups, random_state): """Return a shuffled copy of y eventually shuffle among same groups.""" if groups is None: indices = random_state.permutation(len(y)) else: indices = np.arange(len(groups)) for group in np.unique(groups): this_mask = (groups == group) indices[this_mask] = random_state.permutation(indices[this_mask]) return y[indices] def learning_curve(estimator, X, y, groups=None, train_sizes=np.linspace(0.1, 1.0, 5), cv=None, scoring=None, exploit_incremental_learning=False, n_jobs=1, pre_dispatch="all", verbose=0): """Learning curve. Determines cross-validated training and test scores for different training set sizes. A cross-validation generator splits the whole dataset k times in training and test data. Subsets of the training set with varying sizes will be used to train the estimator and a score for each training subset size and the test set will be computed. Afterwards, the scores will be averaged over all k runs for each training subset size. Read more in the :ref:`User Guide `. Parameters ---------- estimator : object type that implements the "fit" and "predict" methods An object of that type which is cloned for each validation. X : array-like, shape (n_samples, n_features) Training vector, where n_samples is the number of samples and n_features is the number of features. y : array-like, shape (n_samples) or (n_samples, n_features), optional Target relative to X for classification or regression; None for unsupervised learning. groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set. train_sizes : array-like, shape (n_ticks,), dtype float or int Relative or absolute numbers of training examples that will be used to generate the learning curve. If the dtype is float, it is regarded as a fraction of the maximum size of the training set (that is determined by the selected validation method), i.e. it has to be within (0, 1]. Otherwise it is interpreted as absolute sizes of the training sets. Note that for classification the number of samples usually have to be big enough to contain at least one sample from each class. (default: np.linspace(0.1, 1.0, 5)) cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. scoring : string, callable or None, optional, default: None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. exploit_incremental_learning : boolean, optional, default: False If the estimator supports incremental learning, this will be used to speed up fitting for different training set sizes. n_jobs : integer, optional Number of jobs to run in parallel (default 1). pre_dispatch : integer or string, optional Number of predispatched jobs for parallel execution (default is all). The option can reduce the allocated memory. The string can be an expression like '2*n_jobs'. verbose : integer, optional Controls the verbosity: the higher, the more messages. Returns ------- train_sizes_abs : array, shape = (n_unique_ticks,), dtype int Numbers of training examples that has been used to generate the learning curve. Note that the number of ticks might be less than n_ticks because duplicate entries will be removed. train_scores : array, shape (n_ticks, n_cv_folds) Scores on training sets. test_scores : array, shape (n_ticks, n_cv_folds) Scores on test set. Notes ----- See :ref:`examples/model_selection/plot_learning_curve.py ` """ if exploit_incremental_learning and not hasattr(estimator, "partial_fit"): raise ValueError("An estimator must support the partial_fit interface " "to exploit incremental learning") X, y, groups = indexable(X, y, groups) cv = check_cv(cv, y, classifier=is_classifier(estimator)) cv_iter = cv.split(X, y, groups) # Make a list since we will be iterating multiple times over the folds cv_iter = list(cv_iter) scorer = check_scoring(estimator, scoring=scoring) n_max_training_samples = len(cv_iter[0][0]) # Because the lengths of folds can be significantly different, it is # not guaranteed that we use all of the available training data when we # use the first 'n_max_training_samples' samples. train_sizes_abs = _translate_train_sizes(train_sizes, n_max_training_samples) n_unique_ticks = train_sizes_abs.shape[0] if verbose > 0: print("[learning_curve] Training set sizes: " + str(train_sizes_abs)) parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch, verbose=verbose) if exploit_incremental_learning: classes = np.unique(y) if is_classifier(estimator) else None out = parallel(delayed(_incremental_fit_estimator)( clone(estimator), X, y, classes, train, test, train_sizes_abs, scorer, verbose) for train, test in cv.split(X, y, groups)) else: out = parallel(delayed(_fit_and_score)( clone(estimator), X, y, scorer, train[:n_train_samples], test, verbose, parameters=None, fit_params=None, return_train_score=True) for train, test in cv_iter for n_train_samples in train_sizes_abs) out = np.array(out) n_cv_folds = out.shape[0] // n_unique_ticks out = out.reshape(n_cv_folds, n_unique_ticks, 2) out = np.asarray(out).transpose((2, 1, 0)) return train_sizes_abs, out[0], out[1] def _translate_train_sizes(train_sizes, n_max_training_samples): """Determine absolute sizes of training subsets and validate 'train_sizes'. Examples: _translate_train_sizes([0.5, 1.0], 10) -> [5, 10] _translate_train_sizes([5, 10], 10) -> [5, 10] Parameters ---------- train_sizes : array-like, shape (n_ticks,), dtype float or int Numbers of training examples that will be used to generate the learning curve. If the dtype is float, it is regarded as a fraction of 'n_max_training_samples', i.e. it has to be within (0, 1]. n_max_training_samples : int Maximum number of training samples (upper bound of 'train_sizes'). Returns ------- train_sizes_abs : array, shape (n_unique_ticks,), dtype int Numbers of training examples that will be used to generate the learning curve. Note that the number of ticks might be less than n_ticks because duplicate entries will be removed. """ train_sizes_abs = np.asarray(train_sizes) n_ticks = train_sizes_abs.shape[0] n_min_required_samples = np.min(train_sizes_abs) n_max_required_samples = np.max(train_sizes_abs) if np.issubdtype(train_sizes_abs.dtype, np.float): if n_min_required_samples <= 0.0 or n_max_required_samples > 1.0: raise ValueError("train_sizes has been interpreted as fractions " "of the maximum number of training samples and " "must be within (0, 1], but is within [%f, %f]." % (n_min_required_samples, n_max_required_samples)) train_sizes_abs = astype(train_sizes_abs * n_max_training_samples, dtype=np.int, copy=False) train_sizes_abs = np.clip(train_sizes_abs, 1, n_max_training_samples) else: if (n_min_required_samples <= 0 or n_max_required_samples > n_max_training_samples): raise ValueError("train_sizes has been interpreted as absolute " "numbers of training samples and must be within " "(0, %d], but is within [%d, %d]." % (n_max_training_samples, n_min_required_samples, n_max_required_samples)) train_sizes_abs = np.unique(train_sizes_abs) if n_ticks > train_sizes_abs.shape[0]: warnings.warn("Removed duplicate entries from 'train_sizes'. Number " "of ticks will be less than the size of " "'train_sizes' %d instead of %d)." % (train_sizes_abs.shape[0], n_ticks), RuntimeWarning) return train_sizes_abs def _incremental_fit_estimator(estimator, X, y, classes, train, test, train_sizes, scorer, verbose): """Train estimator on training subsets incrementally and compute scores.""" train_scores, test_scores = [], [] partitions = zip(train_sizes, np.split(train, train_sizes)[:-1]) for n_train_samples, partial_train in partitions: train_subset = train[:n_train_samples] X_train, y_train = _safe_split(estimator, X, y, train_subset) X_partial_train, y_partial_train = _safe_split(estimator, X, y, partial_train) X_test, y_test = _safe_split(estimator, X, y, test, train_subset) if y_partial_train is None: estimator.partial_fit(X_partial_train, classes=classes) else: estimator.partial_fit(X_partial_train, y_partial_train, classes=classes) train_scores.append(_score(estimator, X_train, y_train, scorer)) test_scores.append(_score(estimator, X_test, y_test, scorer)) return np.array((train_scores, test_scores)).T def validation_curve(estimator, X, y, param_name, param_range, groups=None, cv=None, scoring=None, n_jobs=1, pre_dispatch="all", verbose=0): """Validation curve. Determine training and test scores for varying parameter values. Compute scores for an estimator with different values of a specified parameter. This is similar to grid search with one parameter. However, this will also compute training scores and is merely a utility for plotting the results. Read more in the :ref:`User Guide `. Parameters ---------- estimator : object type that implements the "fit" and "predict" methods An object of that type which is cloned for each validation. X : array-like, shape (n_samples, n_features) Training vector, where n_samples is the number of samples and n_features is the number of features. y : array-like, shape (n_samples) or (n_samples, n_features), optional Target relative to X for classification or regression; None for unsupervised learning. param_name : string Name of the parameter that will be varied. param_range : array-like, shape (n_values,) The values of the parameter that will be evaluated. groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set. cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. scoring : string, callable or None, optional, default: None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. n_jobs : integer, optional Number of jobs to run in parallel (default 1). pre_dispatch : integer or string, optional Number of predispatched jobs for parallel execution (default is all). The option can reduce the allocated memory. The string can be an expression like '2*n_jobs'. verbose : integer, optional Controls the verbosity: the higher, the more messages. Returns ------- train_scores : array, shape (n_ticks, n_cv_folds) Scores on training sets. test_scores : array, shape (n_ticks, n_cv_folds) Scores on test set. Notes ----- See :ref:`sphx_glr_auto_examples_model_selection_plot_validation_curve.py` """ X, y, groups = indexable(X, y, groups) cv = check_cv(cv, y, classifier=is_classifier(estimator)) scorer = check_scoring(estimator, scoring=scoring) parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch, verbose=verbose) out = parallel(delayed(_fit_and_score)( estimator, X, y, scorer, train, test, verbose, parameters={param_name: v}, fit_params=None, return_train_score=True) for train, test in cv.split(X, y, groups) for v in param_range) out = np.asarray(out) n_params = len(param_range) n_cv_folds = out.shape[0] // n_params out = out.reshape(n_cv_folds, n_params, 2).transpose((2, 1, 0)) return out[0], out[1]