Logistic Regression CV (aka logit, MaxEnt) classifier.

See glossary entry for :term:`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 :class:`~sklearn.model_selection.StratifiedKFold`, but it can be changed using the :term:`cv` parameter. The 'newton-cg', 'sag', 'saga' and 'lbfgs' solvers can warm-start the coefficients (see :term:`Glossary<warm_start>`).

Read more in the :ref:`User Guide <logistic_regression>`.

Parameters ---------- Cs : int 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_intercept : bool, default=True Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.

cv : int 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 :mod:`sklearn.model_selection` module for the list of possible cross-validation objects.

.. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold.

dual : bool, 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' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is only supported by the 'saga' solver.

scoring : str 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 :mod:`sklearn.metrics`. The default scoring option used is 'accuracy'.

solver : 'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga', default='lbfgs'

Algorithm to use in the optimization problem.

• 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' is limited to one-versus-rest schemes.
• 'newton-cg', 'lbfgs' and 'sag' only handle L2 penalty, whereas 'liblinear' and 'saga' handle L1 penalty.
• 'liblinear' might be slower in LogisticRegressionCV because it does not handle warm-starting.

Note that '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.

.. versionadded:: 0.17 Stochastic Average Gradient descent solver. .. versionadded:: 0.19 SAGA solver.

tol : float, default=1e-4 Tolerance for stopping criteria.

max_iter : int, default=100 Maximum number of iterations of the optimization algorithm.

class_weight : dict 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.

.. versionadded:: 0.17 class_weight == 'balanced'

n_jobs : int, default=None Number of CPU cores used during the cross-validation loop. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` for more details.

verbose : int, default=0 For the 'liblinear', 'sag' and 'lbfgs' solvers set verbose to any positive number for verbosity.

refit : bool, 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_scaling : float, 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'.

.. versionadded:: 0.18 Stochastic Average Gradient descent solver for 'multinomial' case. .. versionchanged:: 0.22 Default changed from 'ovr' to 'auto' in 0.22.

random_state : int, 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 :term:`Glossary <random_state>` for details.

l1_ratios : list 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)``.

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...

See also -------- LogisticRegression

Predict confidence scores for samples.

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

Parameters ---------- X : array_like or sparse matrix, shape (n_samples, n_features) Samples.

Returns ------- array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes) Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_1 where >0 means this class would be predicted.

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 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.

y : array-like of shape (n_samples,) Target vector relative to X.

sample_weight : array-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 ------- self : object

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

Predict class labels for samples in X.

Parameters ---------- X : array_like or sparse matrix, shape (n_samples, n_features) Samples.

Returns ------- C : array, shape n_samples Predicted class label per sample.

Predict logarithm of probability estimates.

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

Parameters ---------- X : array-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 ------- T : array-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_``.

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 ---------- X : array-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 ------- T : array-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_``.

Returns the score using the `scoring` option on the given test data and labels.

Parameters ---------- X : array-like of shape (n_samples, n_features) Test samples.

y : array-like of shape (n_samples,) True labels for X.

sample_weight : array-like of shape (n_samples,), default=None Sample weights.

Returns ------- score : float Score of self.predict(X) wrt. y.

Set the parameters of this estimator.

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

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

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.

Attribute classes_: get value or raise Not_found if None.

Attribute classes_: get value as an option.

Attribute coef_: get value or raise Not_found if None.

Attribute coef_: get value as an option.

Attribute intercept_: get value or raise Not_found if None.

Attribute intercept_: get value as an option.

Attribute Cs_: get value or raise Not_found if None.

Attribute Cs_: get value as an option.

Attribute l1_ratios_: get value or raise Not_found if None.

Attribute l1_ratios_: get value as an option.

Attribute coefs_paths_: get value or raise Not_found if None.

Attribute coefs_paths_: get value as an option.

Attribute scores_: get value or raise Not_found if None.

Attribute scores_: get value as an option.

Attribute C_: get value or raise Not_found if None.

Attribute C_: get value as an option.

Attribute l1_ratio_: get value or raise Not_found if None.

Attribute l1_ratio_: get value as an option.

Attribute n_iter_: get value or raise Not_found if None.

Attribute n_iter_: get value as an option.

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.