Model Selection¶

GridSearchCV¶

Exhaustive search over specified parameter values for an estimator. Important members are fit, predict. GridSearchCV implements a “fit” and a “score” method. It also implements “score_samples”, “predict”, “predict_proba”, “decision_function”, “transform” and “inverse_transform” if they are implemented in the estimator used. The parameters of the estimator used to apply these methods are optimized by cross-validated grid-search over a parameter grid. :param estimator: This is assumed to implement the scikit-learn estimator interface.

Either estimator needs to provide a score function, or scoring must be passed.

param param_grid:
type estimator:	estimator object
	Dictionary with parameters names (str) as keys and lists of parameter settings to try as values, or a list of such dictionaries, in which case the grids spanned by each dictionary in the list are explored. This enables searching over any sequence of parameter settings.
type param_grid:
	dict or list of dictionaries
param scoring:	Strategy to evaluate the performance of the cross-validated model on the test set. If scoring represents a single score, one can use: - a single string (see scoring_parameter); - a callable (see scoring) that returns a single value. If scoring represents multiple scores, one can use: - a list or tuple of unique strings; - a callable returning a dictionary where the keys are the metric names and the values are the metric scores; a dictionary with metric names as keys and callables a values.
type scoring:	str, callable, list, tuple or dict, default=None
param n_jobs:	Number of jobs to run in parallel. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors.
type n_jobs:	int, default=None
param refit:	Refit an estimator using the best found parameters on the whole dataset. For multiple metric evaluation, this needs to be a str denoting the scorer that would be used to find the best parameters for refitting the estimator at the end. Where there are considerations other than maximum score in choosing a best estimator, `refit` can be set to a function which returns the selected `best_index_` given `cv_results_`. In that case, the `best_estimator_` and `best_params_` will be set according to the returned `best_index_` while the `best_score_` attribute will not be available. The refitted estimator is made available at the `best_estimator_` attribute and permits using `predict` directly on this `GridSearchCV` instance. Also for multiple metric evaluation, the attributes `best_index_`, `best_score_` and `best_params_` will only be available if `refit` is set and all of them will be determined w.r.t this specific scorer. See `scoring` parameter to know more about multiple metric evaluation.
type refit:	bool, str, or callable, default=True
param cv:	Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross validation, - integer, to specify the number of folds in a (Stratified)KFold, - CV splitter, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if the estimator is a classifier and `y` is either binary or multiclass, `StratifiedKFold` is used. In all other cases, `KFold` is used. These splitters are instantiated with shuffle=False so the splits will be the same across calls. Refer User Guide for the various cross-validation strategies that can be used here.
type cv:	int, cross-validation generator or an iterable, default=None
param verbose:	Controls the verbosity: the higher, the more messages. - >1 : the computation time for each fold and parameter candidate is displayed; >2 : the score is also displayed; >3 : the fold and candidate parameter indexes are also displayed together with the starting time of the computation.
type verbose:	int
param pre_dispatch:
	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 str, giving an expression as a function of n_jobs, as in ‘2*n_jobs’
type pre_dispatch:
	int, or str, default=’2*n_jobs’
param error_score:
	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.
type error_score:
	‘raise’ or numeric, default=np.nan
param return_train_score:
	If `False`, the `cv_results_` attribute will not include training scores. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance.
type return_train_score:
	bool, default=False

cca_zoo.model_selection.GridSearchCV.cv_results_¶

A dict with keys as column headers and values as columns, that can be imported into a pandas DataFrame will be represented by a cv_results_ dict of:

{
'param_kernel': masked_array(data = ['poly', 'poly', 'rbf', 'rbf'],
                             mask = [False False False False]...)
'param_gamma': masked_array(data = [-- -- 0.1 0.2],
                            mask = [ True  True False False]...),
'param_degree': masked_array(data = [2.0 3.0 -- --],
                             mask = [False False  True  True]...),
'split0_test_score'  : [0.80, 0.70, 0.80, 0.93],
'split1_test_score'  : [0.82, 0.50, 0.70, 0.78],
'mean_test_score'    : [0.81, 0.60, 0.75, 0.85],
'std_test_score'     : [0.01, 0.10, 0.05, 0.08],
'rank_test_score'    : [2, 4, 3, 1],
'split0_train_score' : [0.80, 0.92, 0.70, 0.93],
'split1_train_score' : [0.82, 0.55, 0.70, 0.87],
'mean_train_score'   : [0.81, 0.74, 0.70, 0.90],
'std_train_score'    : [0.01, 0.19, 0.00, 0.03],
'mean_fit_time'      : [0.73, 0.63, 0.43, 0.49],
'std_fit_time'       : [0.01, 0.02, 0.01, 0.01],
'mean_score_time'    : [0.01, 0.06, 0.04, 0.04],
'std_score_time'     : [0.00, 0.00, 0.00, 0.01],
'params'             : [{'kernel': 'poly', 'degree': 2}, ...],
}

NOTE The key 'params' is used to store a list of parameter settings dicts for all the parameter candidates. The mean_fit_time, std_fit_time, mean_score_time and std_score_time are all in seconds. For multi-metric evaluation, the scores for all the scorers are available in the cv_results_ dict at the keys ending with that scorer’s name ('_<scorer_name>') instead of '_score' shown above. (‘split0_test_precision’, ‘mean_train_precision’ etc.)

Type:	dict of numpy (masked) ndarrays

cca_zoo.model_selection.GridSearchCV.best_estimator_¶

Estimator that was chosen by the search, i.e. estimator which gave highest score (or smallest loss if specified) on the left out data. Not available if refit=False. See refit parameter for more information on allowed values.

Type:	estimator

cca_zoo.model_selection.GridSearchCV.best_score_¶

Mean cross-validated score of the best_estimator For multi-metric evaluation, this is present only if refit is specified. This attribute is not available if refit is a function.

Type:	float

cca_zoo.model_selection.GridSearchCV.best_params_¶

Parameter setting that gave the best results on the hold out data. For multi-metric evaluation, this is present only if refit is specified.

Type:	dict

cca_zoo.model_selection.GridSearchCV.best_index_¶

The index (of the cv_results_ arrays) which corresponds to the best candidate parameter setting. The dict at search.cv_results_['params'][search.best_index_] gives the parameter setting for the best model, that gives the highest mean score (search.best_score_). For multi-metric evaluation, this is present only if refit is specified.

Type:	int

cca_zoo.model_selection.GridSearchCV.scorer_¶

Scorer function used on the held out data to choose the best parameters for the model. For multi-metric evaluation, this attribute holds the validated scoring dict which maps the scorer key to the scorer callable.

Type:	function or a dict

cca_zoo.model_selection.GridSearchCV.n_splits_¶

The number of cross-validation splits (folds/iterations).

Type:	int

cca_zoo.model_selection.GridSearchCV.refit_time_¶

Seconds used for refitting the best model on the whole dataset. This is present only if refit is not False.

Type:	float

cca_zoo.model_selection.GridSearchCV.multimetric_¶

Whether or not the scorers compute several metrics.

Type:	bool

cca_zoo.model_selection.GridSearchCV.classes_¶

The classes labels. This is present only if refit is specified and the underlying estimator is a classifier.

Type:	ndarray of shape (n_classes,)

cca_zoo.model_selection.GridSearchCV.n_features_in_¶

Number of features seen during fit. Only defined if best_estimator_ is defined (see the documentation for the refit parameter for more details) and that best_estimator_ exposes n_features_in_ when fit.

Type:	int

cca_zoo.model_selection.GridSearchCV.feature_names_in_¶

Names of features seen during fit. Only defined if best_estimator_ is defined (see the documentation for the refit parameter for more details) and that best_estimator_ exposes feature_names_in_ when fit.

Type:	ndarray of shape (n_features_in_,)

Examples

>>> from cca_zoo.model_selection import GridSearchCV
>>> from cca_zoo.models import MCCA
>>> X1 = [[0, 0, 1], [1, 0, 0], [2, 2, 2], [3, 5, 4]]
>>> X2 = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> X3 = [[0, 1, 0], [1, 9, 0], [4, 3, 3,], [12, 8, 10]]
>>> model = MCCA()
>>> params = {'c': [[0.1, 0.2], [0.3, 0.4], 0.1]}
>>> GridSearchCV(model,param_grid=params, cv=3).fit([X1,X2,X3]).best_estimator_.c
[0.1, 0.3, 0.1]

Notes

The parameters selected are those that maximize the score of the left out data, unless an explicit score is passed in which case it is used instead. If n_jobs was set to a value higher than one, the data is copied for each point in the grid (and not n_jobs times). This is done for efficiency reasons if individual jobs take very little time, but may raise errors if the dataset is large and not enough memory is available. A workaround in this case is to set pre_dispatch. Then, the memory is copied only pre_dispatch many times. A reasonable value for pre_dispatch is 2 * n_jobs.

cca_zoo.model_selection.GridSearchCV.classes_

Class labels.

Only available when refit=True and the estimator is a classifier.

cca_zoo.model_selection.GridSearchCV.n_features_in_

Number of features seen during fit.

Only available when refit=True.

RandomizedSearchCV¶

Randomized search on hyper parameters. RandomizedSearchCV implements a “fit” and a “score” method. It also implements “score_samples”, “predict”, “predict_proba”, “decision_function”, “transform” and “inverse_transform” if they are implemented in the estimator used. The parameters of the estimator used to apply these methods are optimized by cross-validated search over parameter settings. In contrast to GridSearchCV, not all parameter values are tried out, but rather a fixed number of parameter settings is sampled from the specified distributions. The number of parameter settings that are tried is given by n_iter. If all parameters are presented as a list, sampling without replacement is performed. If at least one parameter is given as a distribution, sampling with replacement is used. It is highly recommended to use continuous distributions for continuous parameters.

param estimator:
	A object of that type is instantiated for each grid point. This is assumed to implement the scikit-learn estimator interface. Either estimator needs to provide a `score` function, or `scoring` must be passed.
type estimator:	estimator object.
param param_distributions:
	Dictionary with parameters names (str) as keys and distributions or lists of parameters to try. Distributions must provide a `rvs` method for sampling (such as those from scipy.stats.distributions). If a list is given, it is sampled uniformly. If a list of dicts is given, first a dict is sampled uniformly, and then a parameter is sampled using that dict as above.
type param_distributions:
	dict or list of dicts
param n_iter:	Number of parameter settings that are sampled. n_iter trades off runtime vs quality of the solution.
type n_iter:	int, default=10
param scoring:	Strategy to evaluate the performance of the cross-validated model on the test set. If scoring represents a single score, one can use: - a single string (see scoring_parameter); - a callable (see scoring) that returns a single value. If scoring represents multiple scores, one can use: - a list or tuple of unique strings; - a callable returning a dictionary where the keys are the metric names and the values are the metric scores; a dictionary with metric names as keys and callables a values. If None, the estimator’s score method is used.
type scoring:	str, callable, list, tuple or dict, default=None
param n_jobs:	Number of jobs to run in parallel. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors.
type n_jobs:	int, default=None
param refit:	Refit an estimator using the best found parameters on the whole dataset. For multiple metric evaluation, this needs to be a str denoting the scorer that would be used to find the best parameters for refitting the estimator at the end. Where there are considerations other than maximum score in choosing a best estimator, `refit` can be set to a function which returns the selected `best_index_` given the `cv_results`. In that case, the `best_estimator_` and `best_params_` will be set according to the returned `best_index_` while the `best_score_` attribute will not be available. The refitted estimator is made available at the `best_estimator_` attribute and permits using `predict` directly on this `RandomizedSearchCV` instance. Also for multiple metric evaluation, the attributes `best_index_`, `best_score_` and `best_params_` will only be available if `refit` is set and all of them will be determined w.r.t this specific scorer. See `scoring` parameter to know more about multiple metric evaluation.
type refit:	bool, str, or callable, default=True
param cv:	Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross validation, - integer, to specify the number of folds in a (Stratified)KFold, - CV splitter, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if the estimator is a classifier and `y` is either binary or multiclass, `StratifiedKFold` is used. In all other cases, `KFold` is used. These splitters are instantiated with shuffle=False so the splits will be the same across calls. Refer User Guide for the various cross-validation strategies that can be used here.
type cv:	int, cross-validation generator or an iterable, default=None
param verbose:	Controls the verbosity: the higher, the more messages.
type verbose:	int
param pre_dispatch:
	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 str, giving an expression as a function of n_jobs, as in ‘2*n_jobs’
type pre_dispatch:
	int, or str, default=’2*n_jobs’
param random_state:
	Pseudo random number generator state used for random uniform sampling from lists of possible values instead of scipy.stats distributions. Pass an int for reproducible output across multiple function calls.
type random_state:
	int, RandomState instance or None, default=None
param error_score:
	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.
type error_score:
	‘raise’ or numeric, default=np.nan
param return_train_score:
	If `False`, the `cv_results_` attribute will not include training scores. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance.
type return_train_score:
	bool, default=False

cca_zoo.model_selection.RandomizedSearchCV.cv_results_¶

A dict with keys as column headers and values as columns, that can be imported into a pandas DataFrame. will be represented by a cv_results_ dict of:

{
'param_kernel' : masked_array(data = ['rbf', 'rbf', 'rbf'],
                              mask = False),
'param_gamma'  : masked_array(data = [0.1 0.2 0.3], mask = False),
'split0_test_score'  : [0.80, 0.84, 0.70],
'split1_test_score'  : [0.82, 0.50, 0.70],
'mean_test_score'    : [0.81, 0.67, 0.70],
'std_test_score'     : [0.01, 0.24, 0.00],
'rank_test_score'    : [1, 3, 2],
'split0_train_score' : [0.80, 0.92, 0.70],
'split1_train_score' : [0.82, 0.55, 0.70],
'mean_train_score'   : [0.81, 0.74, 0.70],
'std_train_score'    : [0.01, 0.19, 0.00],
'mean_fit_time'      : [0.73, 0.63, 0.43],
'std_fit_time'       : [0.01, 0.02, 0.01],
'mean_score_time'    : [0.01, 0.06, 0.04],
'std_score_time'     : [0.00, 0.00, 0.00],
'params'             : [{'kernel' : 'rbf', 'gamma' : 0.1}, ...],
}

NOTE The key 'params' is used to store a list of parameter settings dicts for all the parameter candidates. The mean_fit_time, std_fit_time, mean_score_time and std_score_time are all in seconds. For multi-metric evaluation, the scores for all the scorers are available in the cv_results_ dict at the keys ending with that scorer’s name ('_<scorer_name>') instead of '_score' shown above. (‘split0_test_precision’, ‘mean_train_precision’ etc.)

Type:	dict of numpy (masked) ndarrays

cca_zoo.model_selection.RandomizedSearchCV.best_estimator_¶

Estimator that was chosen by the search, i.e. estimator which gave highest score (or smallest loss if specified) on the left out data. Not available if refit=False. For multi-metric evaluation, this attribute is present only if refit is specified. See refit parameter for more information on allowed values.

Type:	estimator

cca_zoo.model_selection.RandomizedSearchCV.best_score_¶

Mean cross-validated score of the best_estimator. For multi-metric evaluation, this is not available if refit is False. See refit parameter for more information. This attribute is not available if refit is a function.

Type:	float

cca_zoo.model_selection.RandomizedSearchCV.best_params_¶

Parameter setting that gave the best results on the hold out data. For multi-metric evaluation, this is not available if refit is False. See refit parameter for more information.

Type:	dict

cca_zoo.model_selection.RandomizedSearchCV.best_index_¶

The index (of the cv_results_ arrays) which corresponds to the best candidate parameter setting. The dict at search.cv_results_['params'][search.best_index_] gives the parameter setting for the best model, that gives the highest mean score (search.best_score_). For multi-metric evaluation, this is not available if refit is False. See refit parameter for more information.

Type:	int

cca_zoo.model_selection.RandomizedSearchCV.scorer_¶

Scorer function used on the held out data to choose the best parameters for the model. For multi-metric evaluation, this attribute holds the validated scoring dict which maps the scorer key to the scorer callable.

Type:	function or a dict

cca_zoo.model_selection.RandomizedSearchCV.n_splits_¶

The number of cross-validation splits (folds/iterations).

Type:	int

cca_zoo.model_selection.RandomizedSearchCV.refit_time_¶

Seconds used for refitting the best model on the whole dataset. This is present only if refit is not False.

Type:	float

cca_zoo.model_selection.RandomizedSearchCV.multimetric_¶

Whether or not the scorers compute several metrics.

Type:	bool

cca_zoo.model_selection.RandomizedSearchCV.classes_¶

The classes labels. This is present only if refit is specified and the underlying estimator is a classifier.

Type:	ndarray of shape (n_classes,)

cca_zoo.model_selection.RandomizedSearchCV.n_features_in_¶

Number of features seen during fit. Only defined if best_estimator_ is defined and that best_estimator_ exposes n_features_in_ when fit.

Type:	int

cca_zoo.model_selection.RandomizedSearchCV.feature_names_in_¶

Names of features seen during fit. Only defined if best_estimator_ is defined and that best_estimator_ exposes feature_names_in_ when fit.

Type:	ndarray of shape (n_features_in_,)

Examples

>>> from cca_zoo.model_selection import RandomizedSearchCV
>>> from cca_zoo.models import MCCA
>>> from sklearn.utils.fixes import loguniform
>>> X1 = [[0, 0, 1], [1, 0, 0], [2, 2, 2], [3, 5, 4]]
>>> X2 = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> X3 = [[0, 1, 0], [1, 9, 0], [4, 3, 3,], [12, 8, 10]]
>>> model = MCCA()
>>> params = {'c': [loguniform(1e-4, 1e0), loguniform(1e-4, 1e0), [0.1]]}
>>> def scorer(estimator, X):
...    scores = estimator.score(X)
...    return np.mean(scores)
>>> RandomizedSearchCV(model,param_distributions=params, cv=3, scoring=scorer,n_iter=10).fit([X1,X2,X3]).n_iter
10

Notes

The parameters selected are those that maximize the score of the held-out data, according to the scoring parameter. If n_jobs was set to a value higher than one, the data is copied for each parameter setting(and not n_jobs times). This is done for efficiency reasons if individual jobs take very little time, but may raise errors if the dataset is large and not enough memory is available. A workaround in this case is to set pre_dispatch. Then, the memory is copied only pre_dispatch many times. A reasonable value for pre_dispatch is 2 * n_jobs.

cca_zoo.model_selection.RandomizedSearchCV.classes_

Class labels.

Only available when refit=True and the estimator is a classifier.

cca_zoo.model_selection.RandomizedSearchCV.n_features_in_

Number of features seen during fit.

Only available when refit=True.