sklearn.linear_model.LogisticRegressionCV

class sklearn.linear_model.LogisticRegressionCV(*, Cs=10, fit_intercept=True, cv=None, dual=False, penalty='l2', scoring=None, solver='lbfgs', tol=0.0001, max_iter=100, class_weight=None, n_jobs=None, verbose=0, refit=True, intercept_scaling=1.0, multi_class='auto', random_state=None, l1_ratios=None)

Logistic Regression CV (aka logit, MaxEnt) classifier.

See glossary entry for cross-validation estimator.

This class implements logistic regression using liblinear, newton-cg, sag of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2 regularization with primal formulation. The liblinear solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. Elastic-Net penalty is only supported by the saga solver.

For the grid of Cs values and l1_ratios values, the best hyperparameter is selected by the cross-validator StratifiedKFold, but it can be changed using the cv parameter. The ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers can warm-start the coefficients (see Glossary).

Read more in the User Guide.

Parameters:

Csint or list of floats, default=10

Each of the values in Cs describes the inverse of regularization strength. If Cs is as an int, then a grid of Cs values are chosen in a logarithmic scale between 1e-4 and 1e4. Like in support vector machines, smaller values specify stronger regularization.

fit_interceptbool, default=True

Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.

cvint or cross-validation generator, default=None

The default cross-validation generator used is Stratified K-Folds. If an integer is provided, then it is the number of folds used. See the module sklearn.model_selection module for the list of possible cross-validation objects.

Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.

dualbool, default=False

Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.

penalty{‘l1’, ‘l2’, ‘elasticnet’}, default=’l2’

Specify the norm of the penalty:

• 'l2': add a L2 penalty term (used by default);

• 'l1': add a L1 penalty term;

• 'elasticnet': both L1 and L2 penalty terms are added.

Warning

Some penalties may not work with some solvers. See the parameter solver below, to know the compatibility between the penalty and solver.

scoringstr or callable, default=None

A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). For a list of scoring functions that can be used, look at sklearn.metrics. The default scoring option used is ‘accuracy’.

solver{‘lbfgs’, ‘liblinear’, ‘newton-cg’, ‘newton-cholesky’, ‘sag’, ‘saga’}, default=’lbfgs’

Algorithm to use in the optimization problem. Default is ‘lbfgs’. To choose a solver, you might want to consider the following aspects:

• For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ and ‘saga’ are faster for large ones;

• For multiclass problems, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss;

• ‘liblinear’ might be slower in LogisticRegressionCV because it does not handle warm-starting. ‘liblinear’ is limited to one-versus-rest schemes.

• ‘newton-cholesky’ is a good choice for n_samples >> n_features, especially with one-hot encoded categorical features with rare categories. Note that it is limited to binary classification and the one-versus-rest reduction for multiclass classification. Be aware that the memory usage of this solver has a quadratic dependency on n_features because it explicitly computes the Hessian matrix.

Warning

The choice of the algorithm depends on the penalty chosen. Supported penalties by solver:

• ‘lbfgs’ - [‘l2’]

• ‘liblinear’ - [‘l1’, ‘l2’]

• ‘newton-cg’ - [‘l2’]

• ‘newton-cholesky’ - [‘l2’]

• ‘sag’ - [‘l2’]

• ‘saga’ - [‘elasticnet’, ‘l1’, ‘l2’]

Note

‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

New in version 1.2: newton-cholesky solver.

tolfloat, default=1e-4

Tolerance for stopping criteria.

max_iterint, default=100

Maximum number of iterations of the optimization algorithm.

class_weightdict or ‘balanced’, default=None

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

New in version 0.17: class_weight == ‘balanced’

n_jobsint, default=None

Number of CPU cores used during the cross-validation loop. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

verboseint, default=0

For the ‘liblinear’, ‘sag’ and ‘lbfgs’ solvers set verbose to any positive number for verbosity.

refitbool, default=True

If set to True, the scores are averaged across all folds, and the coefs and the C that corresponds to the best score is taken, and a final refit is done using these parameters. Otherwise the coefs, intercepts and C that correspond to the best scores across folds are averaged.

intercept_scalingfloat, default=1

Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.

Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.

multi_class{‘auto, ‘ovr’, ‘multinomial’}, default=’auto’

If the option chosen is ‘ovr’, then a binary problem is fit for each label. For ‘multinomial’ the loss minimised is the multinomial loss fit across the entire probability distribution, even when the data is binary. ‘multinomial’ is unavailable when solver=’liblinear’. ‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’, and otherwise selects ‘multinomial’.

New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.

Changed in version 0.22: Default changed from ‘ovr’ to ‘auto’ in 0.22.

random_stateint, RandomState instance, default=None

Used when solver='sag', ‘saga’ or ‘liblinear’ to shuffle the data. Note that this only applies to the solver and not the cross-validation generator. See Glossary for details.

l1_ratioslist of float, default=None

The list of Elastic-Net mixing parameter, with 0 <= l1_ratio <= 1. Only used if penalty='elasticnet'. A value of 0 is equivalent to using penalty='l2', while 1 is equivalent to using penalty='l1'. For 0 < l1_ratio <1, the penalty is a combination of L1 and L2.

Attributes:

classes_ndarray of shape (n_classes, )

A list of class labels known to the classifier.

coef_ndarray of shape (1, n_features) or (n_classes, n_features)

Coefficient of the features in the decision function.

coef_ is of shape (1, n_features) when the given problem is binary.

intercept_ndarray of shape (1,) or (n_classes,)

Intercept (a.k.a. bias) added to the decision function.

If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape(1,) when the problem is binary.

Cs_ndarray of shape (n_cs)

Array of C i.e. inverse of regularization parameter values used for cross-validation.

l1_ratios_ndarray of shape (n_l1_ratios)

Array of l1_ratios used for cross-validation. If no l1_ratio is used (i.e. penalty is not ‘elasticnet’), this is set to [None]

coefs_paths_ndarray of shape (n_folds, n_cs, n_features) or (n_folds, n_cs, n_features + 1)

dict with classes as the keys, and the path of coefficients obtained during cross-validating across each fold and then across each Cs after doing an OvR for the corresponding class as values. If the ‘multi_class’ option is set to ‘multinomial’, then the coefs_paths are the coefficients corresponding to each class. Each dict value has shape (n_folds, n_cs, n_features) or (n_folds, n_cs, n_features + 1) depending on whether the intercept is fit or not. If penalty='elasticnet', the shape is (n_folds, n_cs, n_l1_ratios_, n_features) or (n_folds, n_cs, n_l1_ratios_, n_features + 1).

scores_dict

dict with classes as the keys, and the values as the grid of scores obtained during cross-validating each fold, after doing an OvR for the corresponding class. If the ‘multi_class’ option given is ‘multinomial’ then the same scores are repeated across all classes, since this is the multinomial class. Each dict value has shape (n_folds, n_cs) or (n_folds, n_cs, n_l1_ratios) if penalty='elasticnet'.

C_ndarray of shape (n_classes,) or (n_classes - 1,)

Array of C that maps to the best scores across every class. If refit is set to False, then for each class, the best C is the average of the C’s that correspond to the best scores for each fold. C_ is of shape(n_classes,) when the problem is binary.

l1_ratio_ndarray of shape (n_classes,) or (n_classes - 1,)

Array of l1_ratio that maps to the best scores across every class. If refit is set to False, then for each class, the best l1_ratio is the average of the l1_ratio’s that correspond to the best scores for each fold. l1_ratio_ is of shape(n_classes,) when the problem is binary.

n_iter_ndarray of shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs)

Actual number of iterations for all classes, folds and Cs. In the binary or multinomial cases, the first dimension is equal to 1. If penalty='elasticnet', the shape is (n_classes, n_folds, n_cs, n_l1_ratios) or (1, n_folds, n_cs, n_l1_ratios).

n_features_in_int

Number of features seen during fit.

New in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

New in version 1.0.

See also

LogisticRegression

Logistic regression without tuning the hyperparameter C.

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.linear_model import LogisticRegressionCV
>>> X, y = load_iris(return_X_y=True)
>>> clf = LogisticRegressionCV(cv=5, random_state=0).fit(X, y)
>>> clf.predict(X[:2, :])
array([0, 0])
>>> clf.predict_proba(X[:2, :]).shape
(2, 3)
>>> clf.score(X, y)
0.98...

Methods

decision_function(X)	Predict confidence scores for samples.
densify()	Convert coefficient matrix to dense array format.
fit(X, y[, sample_weight])	Fit the model according to the given training data.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict class labels for samples in X.
predict_log_proba(X)	Predict logarithm of probability estimates.
predict_proba(X)	Probability estimates.
score(X, y[, sample_weight])	Score using the scoring option on the given test data and labels.
set_params(**params)	Set the parameters of this estimator.
sparsify()	Convert coefficient matrix to sparse format.

decision_function(X)

Predict confidence scores for samples.

The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data matrix for which we want to get the confidence scores.

Returns:

scoresndarray of shape (n_samples,) or (n_samples, n_classes)

Confidence scores per (n_samples, n_classes) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.

densify()

Convert coefficient matrix to dense array format.

Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.

Returns:

self

Fitted estimator.

fit(X, y, sample_weight=None)

Fit the model according to the given training data.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

Training vector, where n_samples is the number of samples and n_features is the number of features.

yarray-like of shape (n_samples,)

Target vector relative to X.

sample_weightarray-like of shape (n_samples,) default=None

Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.

Returns:

selfobject

Fitted LogisticRegressionCV estimator.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

predict(X)

Predict class labels for samples in X.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data matrix for which we want to get the predictions.

Returns:

y_predndarray of shape (n_samples,)

Vector containing the class labels for each sample.

predict_log_proba(X)

Predict logarithm of probability estimates.

The returned estimates for all classes are ordered by the label of classes.

Parameters:

Xarray-like of shape (n_samples, n_features)

Vector to be scored, where n_samples is the number of samples and n_features is the number of features.

Returns:

Tarray-like of shape (n_samples, n_classes)

Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.

predict_proba(X)

Probability estimates.

The returned estimates for all classes are ordered by the label of classes.

For a multi_class problem, if multi_class is set to be “multinomial” the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes.

Parameters:

Xarray-like of shape (n_samples, n_features)

Vector to be scored, where n_samples is the number of samples and n_features is the number of features.

Returns:

Tarray-like of shape (n_samples, n_classes)

Returns the probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.

score(X, y, sample_weight=None)

Score using the scoring option on the given test data and labels.

Parameters:

Xarray-like of shape (n_samples, n_features)

Test samples.

yarray-like of shape (n_samples,)

True labels for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:

scorefloat

Score of self.predict(X) w.r.t. y.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

sparsify()

Convert coefficient matrix to sparse format.

Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.

The intercept_ member is not converted.

Returns:

self

Fitted estimator.

Notes

For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.

After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.

Examples using sklearn.linear_model.LogisticRegressionCV

Importance of Feature Scaling

Importance of Feature Scaling