8.15.2.5. sklearn.linear_model.LogisticRegression

class sklearn.linear_model.LogisticRegression(penalty='l2', dual=False, tol=0.0001, C=None, fit_intercept=True, intercept_scaling=1, scale_C=True, class_weight=None)

Logistic Regression (aka logit, MaxEnt) classifier.

In the multiclass case, the training algorithm uses a one-vs.-all (OvA) scheme, rather than the “true” multinomial LR.

This class implements L1 and L2 regularized logistic regression using the liblinear library. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).

Parameters :

penalty : string, ‘l1’ or ‘l2’

Used to specify the norm used in the penalization

dual : boolean

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

C : float or None, optional (default=None)

Specifies the strength of the regularization. The smaller it is the bigger in the regularization. If None then C is set to n_samples.

fit_intercept : bool, default: True

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

intercept_scaling : float, default: 1

when self.fit_intercept is True, instance vector 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

tol: float, optional :

tolerance for stopping criteria

scale_C : bool, default: True

Scale C with number of samples. It makes the setting of C independent of the number of samples. To match liblinear commandline one should use scale_C=False. WARNING: scale_C will disappear in version 0.12.

See also

LinearSVC

Notes

The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon, to have slightly different results for the same input data. If that happens, try with a smaller tol parameter.

References:

LIBLINEAR – A Library for Large Linear Classification

http://www.csie.ntu.edu.tw/~cjlin/liblinear/

Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent

methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf

Attributes

coef_	array, shape = [n_classes-1, n_features]	Coefficient of the features in the decision function. coef_ is readonly property derived from raw_coef_ that follows the internal memory layout of liblinear.
intercept_	array, shape = [n_classes-1]	intercept (a.k.a. bias) added to the decision function. It is available only when parameter intercept is set to True
scaled_C_	float	The C value passed to liblinear.

Methods

decision_function(X)	Decision function value for X according to the trained model.
fit(X, y[, class_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 the estimator
predict(X)	Predict target values of X according to the fitted model.
predict_log_proba(X)	Log of Probability estimates.
predict_proba(X)	Probability estimates.
score(X, y)	Returns the mean accuracy on the given test data and labels.
set_params(**params)	Set the parameters of the estimator.
transform(X[, threshold])	Reduce X to its most important features.

__init__(penalty='l2', dual=False, tol=0.0001, C=None, fit_intercept=True, intercept_scaling=1, scale_C=True, class_weight=None)

decision_function(X)

Decision function value for X according to the trained model.

Parameters :

X : array-like, shape = [n_samples, n_features]

Returns :

T : array-like, shape = [n_samples, n_class]

Returns the decision function of the sample for each class in the model.

fit(X, y, class_weight=None)

Fit the model according to the given training data.

Parameters :

X : {array-like, 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 : array-like, shape = [n_samples]

Target vector relative to X

class_weight : {dict, ‘auto’}, optional

Weights associated with classes. If not given, all classes are supposed to have weight one.

Returns :

self : object

Returns self.

fit_transform(X, y=None, **fit_params)

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.

Notes

This method just calls fit and transform consecutively, i.e., it is not an optimized implementation of fit_transform, unlike other transformers such as PCA.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

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

predict(X)

Predict target values of X according to the fitted model.

Parameters :X : {array-like, sparse matrix}, shape = [n_samples, n_features] Returns :C : array, shape = [n_samples]

predict_log_proba(X)

Log of Probability estimates.

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

Parameters :

X : array-like, shape = [n_samples, n_features]

Returns :

T : array-like, shape = [n_samples, n_classes]

Returns the log-probabilities of the sample for each class in the model, where classes are ordered by arithmetical order.

predict_proba(X)

Probability estimates.

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

Parameters :

X : array-like, shape = [n_samples, n_features]

Returns :

T : array-like, shape = [n_samples, n_classes]

Returns the probability of the sample for each class in the model, where classes are ordered by arithmetical order.

score(X, y)

Returns the mean accuracy on the given test data and labels.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Labels for X.

Returns :

z : float

set_params(**params)

Set the parameters of the 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 :

transform(X, threshold=None)

Reduce X to its most important features.

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.