3.2.4.1.5. 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=1, verbose=0, refit=True, intercept_scaling=1.0, multi_class='ovr', random_state=None)[source]¶ Logistic Regression CV (aka logit, MaxEnt) classifier.
This class implements logistic regression using liblinear, newtoncg, sag of lbfgs optimizer. The newtoncg, 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.
For the grid of Cs values (that are set by default to be ten values in a logarithmic scale between 1e4 and 1e4), the best hyperparameter is selected by the crossvalidator StratifiedKFold, but it can be changed using the cv parameter. In the case of newtoncg and lbfgs solvers, we warm start along the path i.e guess the initial coefficients of the present fit to be the coefficients got after convergence in the previous fit, so it is supposed to be faster for highdimensional dense data.
For a multiclass problem, the hyperparameters for each class are computed using the best scores got by doing a onevsrest in parallel across all folds and classes. Hence this is not the true multinomial loss.
Read more in the User Guide.
Parameters: Cs : list of floats  int
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 1e4 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.
class_weight : dict or ‘balanced’, optional
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’
cv : integer or crossvalidation generator
The default crossvalidation generator used is Stratified KFolds. If an integer is provided, then it is the number of folds used. See the module
sklearn.cross_validation
module for the list of possible crossvalidation objects.penalty : str, ‘l1’ or ‘l2’
Used to specify the norm used in the penalization. The newtoncg and lbfgs solvers support only l2 penalties.
dual : bool
Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
scoring : callabale
Scoring function to use as crossvalidation criteria. For a list of scoring functions that can be used, look at
sklearn.metrics
. The default scoring option used is accuracy_score.solver : {‘newtoncg’, ‘lbfgs’, ‘liblinear’, ‘sag’}
Algorithm to use in the optimization problem.
 For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ is
faster for large ones.
 For multiclass problems, only ‘newtoncg’ and ‘lbfgs’ handle
multinomial loss; ‘sag’ and ‘liblinear’ are limited to oneversusrest schemes.
‘newtoncg’, ‘lbfgs’ and ‘sag’ only handle L2 penalty.
 ‘liblinear’ might be slower in LogisticRegressionCV because it does
not handle warmstarting.
tol : float, optional
Tolerance for stopping criteria.
max_iter : int, optional
Maximum number of iterations of the optimization algorithm.
n_jobs : int, optional
Number of CPU cores used during the crossvalidation loop. If given a value of 1, all cores are used.
verbose : int
For the ‘liblinear’, ‘sag’ and ‘lbfgs’ solvers set verbose to any positive number for verbosity.
refit : bool
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.
multi_class : str, {‘ovr’, ‘multinomial’}
Multiclass option can be either ‘ovr’ or ‘multinomial’. If the option chosen is ‘ovr’, then a binary problem is fit for each label. Else the loss minimised is the multinomial loss fit across the entire probability distribution. Works only for ‘lbfgs’ and ‘newtoncg’ solvers.
intercept_scaling : float, default 1.
Useful only if solver is liblinear. This parameter is 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 equals 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.
random_state : int seed, RandomState instance, or None (default)
The seed of the pseudo random number generator to use when shuffling the data.
Attributes: coef_ : array, 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. coef_ is readonly property derived from raw_coef_ that follows the internal memory layout of liblinear.
intercept_ : array, shape (1,) or (n_classes,)
Intercept (a.k.a. bias) added to the decision function. It is available only when parameter intercept is set to True and is of shape(1,) when the problem is binary.
Cs_ : array
Array of C i.e. inverse of regularization parameter values used for crossvalidation.
coefs_paths_ : array, shape
(n_folds, len(Cs_), n_features)
or(n_folds, len(Cs_), n_features + 1)
dict with classes as the keys, and the path of coefficients obtained during crossvalidating 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, len(Cs_), n_features)
or(n_folds, len(Cs_), n_features + 1)
depending on whether the intercept is fit or not.scores_ : dict
dict with classes as the keys, and the values as the grid of scores obtained during crossvalidating 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, len(Cs))
C_ : array, 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.
n_iter_ : array, 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.
See also
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. fit_transform
(X[, y])Fit to data, then transform it. get_params
([deep])Get parameters for this estimator. predict
(X)Predict class labels for samples in X. predict_log_proba
(X)Log of probability estimates. predict_proba
(X)Probability estimates. score
(X, y[, sample_weight])Returns the mean accuracy on the given test data and labels. set_params
(**params)Set the parameters of this estimator. sparsify
()Convert coefficient matrix to sparse format. transform
(*args, **kwargs)DEPRECATED: Support to use estimators as feature selectors will be removed in version 0.19. 
__init__
(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=1, verbose=0, refit=True, intercept_scaling=1.0, multi_class='ovr', random_state=None)[source]¶

decision_function
(X)[source]¶ Predict confidence scores for samples.
The confidence score for a sample is the signed distance of that sample to the hyperplane.
Parameters: X : {arraylike, 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.

densify
()[source]¶ Convert coefficient matrix to dense array format.
Converts the
coef_
member (back) to a numpy.ndarray. This is the default format ofcoef_
and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a noop.Returns: self: estimator :

fit
(X, y, sample_weight=None)[source]¶ Fit the model according to the given training data.
Parameters: X : {arraylike, sparse matrix}, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples and n_features is the number of features.
y : arraylike, shape (n_samples,)
Target vector relative to X.
sample_weight : arraylike, shape (n_samples,) optional
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
Returns: self : object
Returns self.

fit_transform
(X, y=None, **fit_params)[source]¶ Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.
Parameters: X : numpy array of shape [n_samples, n_features]
Training set.
y : numpy array of shape [n_samples]
Target values.
Returns: X_new : numpy array of shape [n_samples, n_features_new]
Transformed array.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
Parameters: deep: boolean, optional :
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
(X)[source]¶ Predict class labels for samples in X.
Parameters: X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
Samples.
Returns: C : array, shape = [n_samples]
Predicted class label per sample.

predict_log_proba
(X)[source]¶ Log of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
Parameters: X : arraylike, shape = [n_samples, n_features]
Returns: T : arraylike, shape = [n_samples, n_classes]
Returns the logprobability of the sample for each class in the model, where classes are ordered as they are in
self.classes_
.

predict_proba
(X)[source]¶ 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 onevsrest 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 : arraylike, shape = [n_samples, n_features]
Returns: T : arraylike, 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)[source]¶ Returns the mean accuracy on the given test data and labels.
In multilabel classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
Parameters: X : arraylike, shape = (n_samples, n_features)
Test samples.
y : arraylike, shape = (n_samples) or (n_samples, n_outputs)
True labels for X.
sample_weight : arraylike, shape = [n_samples], optional
Sample weights.
Returns: score : float
Mean accuracy of self.predict(X) wrt. y.

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object.Returns: self :

sparsify
()[source]¶ Convert coefficient matrix to sparse format.
Converts the
coef_
member to a scipy.sparse matrix, which for L1regularized models can be much more memory and storageefficient than the usual numpy.ndarray representation.The
intercept_
member is not converted.Returns: self: estimator : Notes
For nonsparse 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.

transform
(*args, **kwargs)[source]¶ DEPRECATED: Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.
Reduce X to its most important features.
Usescoef_
orfeature_importances_
to determine the most important features. For models with acoef_
for each class, the absolute sum over the classes is used.Parameters: X : array or scipy sparse matrix of shape [n_samples, n_features]
The input samples.
 threshold : string, float or None, optional (default=None)
The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if available, the object attribute
threshold
is used. Otherwise, “mean” is used by default.
Returns: X_r : array of shape [n_samples, n_selected_features]
The input samples with only the selected features.