LogisticRegressionCV #

classsklearn.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='deprecated',random_state=None,l1_ratios=None)[source]#

Logistic Regression CV (aka logit, MaxEnt) classifier.

See glossary entry forcross-validation estimator.

This class implements logistic regression using liblinear, newton-cg, sagor lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2regularization with primal formulation. The liblinear solver supports bothL1 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 ofCs values andl1_ratios values, the best hyperparameteris selected by the cross-validatorStratifiedKFold, but it can be changedusing thecv parameter. The ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’solvers can warm-start the coefficients (seeGlossary).

Read more in theUser Guide.

Parameters:

Csint or list of floats, default=10

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

fit_interceptbool, default=True

Specifies if a constant (a.k.a. bias or intercept) should beadded 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 modulesklearn.model_selection module for thelist 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 (constrained) or primal (regularized, see alsothis equation) formulation. Dual formulationis only implemented for l2 penalty with liblinear solver. Prefer dual=False whenn_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 parametersolver below, to know the compatibility between the penalty andsolver.

scoringstr or callable, default=None

The scoring method to use for cross-validation. Options:

str: seeString name scorers for options.
callable: a scorer callable object (e.g., function) with signaturescorer(estimator,X,y). SeeCallable scorers for details.
None:accuracy is used.

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, all solvers except ‘liblinear’ minimize the fullmultinomial loss;
‘liblinear’ might be slower inLogisticRegressionCVbecause it does not handle warm-starting.
‘liblinear’ can only handle binary classification by default. To apply aone-versus-rest scheme for the multiclass setting one can wrap it with theOneVsRestClassifier.
‘newton-cholesky’ is a good choice forn_samples >>n_features*n_classes, especially with one-hot encodedcategorical features with rare categories. Be aware that the memory usageof this solver has a quadratic dependency onn_features*n_classesbecause it explicitly computes the full Hessian matrix.

Warning

The choice of the algorithm depends on the penalty chosen and on(multinomial) multiclass support:

solver	penalty	multinomial multiclass
‘lbfgs’	‘l2’	yes
‘liblinear’	‘l1’, ‘l2’	no
‘newton-cg’	‘l2’	yes
‘newton-cholesky’	‘l2’,	yes
‘sag’	‘l2’,	yes
‘saga’	‘elasticnet’, ‘l1’, ‘l2’	yes

Note

‘sag’ and ‘saga’ fast convergence is only guaranteed on featureswith approximately the same scale. You can preprocess the data witha scaler fromsklearn.preprocessing.

Added in version 0.17:Stochastic Average Gradient (SAG) descent solver. Multinomial support inversion 0.18.

Added in version 0.19:SAGA solver.

Added in version 1.2:newton-cholesky solver. Multinomial support in version 1.6.

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 adjustweights inversely proportional to class frequencies in the input dataasn_samples/(n_classes*np.bincount(y)).

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

Added 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 ajoblib.parallel_backend context.-1 means using all processors. SeeGlossaryfor more details.

verboseint, default=0

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

refitbool, default=True

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

intercept_scalingfloat, default=1

Useful only when the solverliblinear is usedandself.fit_intercept is set toTrue. In this case,x becomes[x,self.intercept_scaling],i.e. a “synthetic” feature with constant value equal tointercept_scaling is appended to the instance vector.The intercept becomesintercept_scaling*synthetic_feature_weight.

Note

The synthetic feature weight is subject to L1 or L2regularization 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 eachlabel. For ‘multinomial’ the loss minimised is the multinomial loss fitacross the entire probability distribution,even when the data isbinary. ‘multinomial’ is unavailable when solver=’liblinear’.‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’,and otherwise selects ‘multinomial’.

Added 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.

Deprecated since version 1.5:multi_class was deprecated in version 1.5 and will be removed in 1.8.From then on, the recommended ‘multinomial’ will always be used forn_classes>=3.Solvers that do not support ‘multinomial’ will raise an error.Usesklearn.multiclass.OneVsRestClassifier(LogisticRegressionCV()) if youstill want to use OvR.

random_stateint, RandomState instance, default=None

Used whensolver='sag', ‘saga’ or ‘liblinear’ to shuffle the data.Note that this only applies to the solver and not the cross-validationgenerator. SeeGlossary for details.

l1_ratioslist of float, default=None

The list of Elastic-Net mixing parameter, with0<=l1_ratio<=1.Only used ifpenalty='elasticnet'. A value of 0 is equivalent tousingpenalty='l2', while 1 is equivalent to usingpenalty='l1'. For0<l1_ratio<1, the penalty is a combinationof 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 problemis binary.

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

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

Iffit_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 usedfor 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 obtainedduring cross-validating across each fold and then across each Csafter doing an OvR for the corresponding class as values.If the ‘multi_class’ option is set to ‘multinomial’, thenthe 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 theintercept is fit or not. Ifpenalty='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 thegrid of scores obtained during cross-validating each fold, after doingan OvR for the corresponding class. If the ‘multi_class’ optiongiven is ‘multinomial’ then the same scores are repeated acrossall classes, since this is the multinomial class. Each dict valuehas shape(n_folds,n_cs) or(n_folds,n_cs,n_l1_ratios) ifpenalty='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 isset to False, then for each class, the best C is the average of theC’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. Ifrefit is set to False, then for each class, the best l1_ratio is theaverage of the l1_ratio’s that correspond to the best scores for eachfold.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.Ifpenalty='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 duringfit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen duringfit. Defined only whenXhas feature names that are all strings.

Added in version 1.0.

See also

LogisticRegression: Logistic regression without tuning the hyperparameterC.

Examples

>>>fromsklearn.datasetsimportload_iris>>>fromsklearn.linear_modelimportLogisticRegressionCV>>>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...

decision_function(X)[source]#

Predict confidence scores for samples.

The confidence score for a sample is proportional to the signeddistance 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 thebinary case, confidence score forself.classes_[1] where >0 meansthis class would be predicted.

densify()[source]#

Convert coefficient matrix to dense array format.

Converts thecoef_ member (back) to a numpy.ndarray. This is thedefault format ofcoef_ and is required for fitting, so callingthis method is only required on models that have previously beensparsified; otherwise, it is a no-op.

Returns:

self: Fitted estimator.

fit(X,y,sample_weight=None,**params)[source]#

Fit the model according to the given training data.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): Training vector, wheren_samples is the number of samples andn_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.
**paramsdict: Parameters to pass to the underlying splitter and scorer.
Added in version 1.4.

Returns:

selfobject: Fitted LogisticRegressionCV estimator.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Added in version 1.4.

Returns:

routingMetadataRouter: AMetadataRouter encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

predict(X)[source]#

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)[source]#

Predict logarithm of probability estimates.

The returned estimates for all classes are ordered by thelabel of classes.

Parameters:

Xarray-like of shape (n_samples, n_features): Vector to be scored, wheren_samples is the number of samples andn_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 themodel, where classes are ordered as they are inself.classes_.

predict_proba(X)[source]#

Probability estimates.

The returned estimates for all classes are ordered by thelabel 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 ofeach class.Else use a one-vs-rest approach, i.e. calculate the probabilityof each class assuming it to be positive using the logistic functionand normalize these values across all the classes.

Parameters:

Xarray-like of shape (n_samples, n_features): Vector to be scored, wheren_samples is the number of samples andn_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 inself.classes_.

score(X,y,sample_weight=None,**score_params)[source]#

Score using thescoring 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.
**score_paramsdict: Parameters to pass to thescore method of the underlying scorer.
Added in version 1.4.

Returns:

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

set_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→LogisticRegressionCV[source]#

Configure whether metadata should be requested to be passed to thefit method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

True: metadata is requested, and passed tofit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it tofit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter infit.

Returns:

selfobject: The updated object.

set_params(**params)[source]#

Set the parameters of this estimator.

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

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

set_score_request(*,sample_weight:bool|None|str='$UNCHANGED$')→LogisticRegressionCV[source]#

Configure whether metadata should be requested to be passed to thescore method.

The options for each parameter are:

True: metadata is requested, and passed toscore if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it toscore.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter inscore.

Returns:

selfobject: The updated object.

sparsify()[source]#

Convert coefficient matrix to sparse format.

Converts thecoef_ member to a scipy.sparse matrix, which forL1-regularized models can be much more memory- and storage-efficientthan the usual numpy.ndarray representation.

Theintercept_ member is not converted.

Returns:

self: Fitted estimator.

Notes

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

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

Gallery examples#

Comparison of Calibration of Classifiers

Importance of Feature Scaling

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