sklearn.linear_model
.LogisticRegression¶

class
sklearn.linear_model.
LogisticRegression
(penalty='l2', dual=False, tol=0.0001, C=1.0, fit_intercept=True, intercept_scaling=1, class_weight=None, random_state=None, solver='lbfgs', max_iter=100, multi_class='auto', verbose=0, warm_start=False, n_jobs=None, l1_ratio=None)[source]¶ Logistic Regression (aka logit, MaxEnt) classifier.
In the multiclass case, the training algorithm uses the onevsrest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the crossentropy loss if the ‘multi_class’ option is set to ‘multinomial’. (Currently the ‘multinomial’ option is supported only by the ‘lbfgs’, ‘sag’, ‘saga’ and ‘newtoncg’ solvers.)
This class implements regularized logistic regression using the ‘liblinear’ library, ‘newtoncg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers. Note that regularization is applied by default. It can handle both dense and sparse input. Use Cordered arrays or CSR matrices containing 64bit floats for optimal performance; any other input format will be converted (and copied).
The ‘newtoncg’, ‘sag’, and ‘lbfgs’ solvers support only L2 regularization with primal formulation, or no regularization. The ‘liblinear’ solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. The ElasticNet regularization is only supported by the ‘saga’ solver.
Read more in the User Guide.
 Parameters
 penalty{‘l1’, ‘l2’, ‘elasticnet’, ‘none’}, default=’l2’
Used to specify the norm used in the penalization. The ‘newtoncg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties. ‘elasticnet’ is only supported by the ‘saga’ solver. If ‘none’ (not supported by the liblinear solver), no regularization is applied.
New in version 0.19: l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)
 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.
 tolfloat, default=1e4
Tolerance for stopping criteria.
 Cfloat, default=1.0
Inverse of regularization strength; must be a positive float. 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.
 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.
 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’
 random_stateint, RandomState instance, default=None
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by
np.random
. Used whensolver
== ‘sag’ or ‘liblinear’. solver{‘newtoncg’, ‘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 ‘newtoncg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss; ‘liblinear’ is limited to oneversusrest schemes.
‘newtoncg’, ‘lbfgs’, ‘sag’ and ‘saga’ handle L2 or no penalty
‘liblinear’ and ‘saga’ also handle L1 penalty
‘saga’ also supports ‘elasticnet’ penalty
‘liblinear’ does not support setting
penalty='none'
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.
New in version 0.17: Stochastic Average Gradient descent solver.
New in version 0.19: SAGA solver.
Changed in version 0.22: The default solver changed from ‘liblinear’ to ‘lbfgs’ in 0.22.
 max_iterint, default=100
Maximum number of iterations taken for the solvers to converge.
 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.
 verboseint, default=0
For the liblinear and lbfgs solvers set verbose to any positive number for verbosity.
 warm_startbool, default=False
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. Useless for liblinear solver. See the Glossary.
New in version 0.17: warm_start to support lbfgs, newtoncg, sag, saga solvers.
 n_jobsint, default=None
Number of CPU cores used when parallelizing over classes if multi_class=’ovr’”. This parameter is ignored when the
solver
is set to ‘liblinear’ regardless of whether ‘multi_class’ is specified or not.None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. l1_ratiofloat, default=None
The ElasticNet mixing parameter, with
0 <= l1_ratio <= 1
. Only used ifpenalty='elasticnet'`. Setting ``l1_ratio=0
is equivalent to usingpenalty='l2'
, while settingl1_ratio=1
is equivalent to usingpenalty='l1'
. For0 < 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. In particular, whenmulti_class='multinomial'
,coef_
corresponds to outcome 1 (True) andcoef_
corresponds to outcome 0 (False). 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 given problem is binary. In particular, whenmulti_class='multinomial'
,intercept_
corresponds to outcome 1 (True) andintercept_
corresponds to outcome 0 (False). n_iter_ndarray of shape (n_classes,) or (1, )
Actual number of iterations for all classes. If binary or multinomial, it returns only 1 element. For liblinear solver, only the maximum number of iteration across all classes is given.
Changed in version 0.20: In SciPy <= 1.0.0 the number of lbfgs iterations may exceed
max_iter
.n_iter_
will now report at mostmax_iter
.
See also
SGDClassifier
Incrementally trained logistic regression (when given the parameter
loss="log"
).LogisticRegressionCV
Logistic regression with builtin cross validation.
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.
Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.
References
 LBFGSB – Software for Largescale Boundconstrained Optimization
Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html
 LIBLINEAR – A Library for Large Linear Classification
 SAG – Mark Schmidt, Nicolas Le Roux, and Francis Bach
Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal00860051/document
 SAGA – Defazio, A., Bach F. & LacosteJulien S. (2014).
SAGA: A Fast Incremental Gradient Method With Support for NonStrongly Convex Composite Objectives https://arxiv.org/abs/1407.0202
 HsiangFu Yu, FangLan Huang, ChihJen Lin (2011). Dual coordinate descent
methods for logistic regression and maximum entropy models. Machine Learning 85(12):4175. https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf
Examples
>>> from sklearn.datasets import load_iris >>> from sklearn.linear_model import LogisticRegression >>> X, y = load_iris(return_X_y=True) >>> clf = LogisticRegression(random_state=0).fit(X, y) >>> clf.predict(X[:2, :]) array([0, 0]) >>> clf.predict_proba(X[:2, :]) array([[9.8...e01, 1.8...e02, 1.4...e08], [9.7...e01, 2.8...e02, ...e08]]) >>> clf.score(X, y) 0.97...
Methods
decision_function
(self, X)Predict confidence scores for samples.
densify
(self)Convert coefficient matrix to dense array format.
fit
(self, X, y[, sample_weight])Fit the model according to the given training data.
get_params
(self[, deep])Get parameters for this estimator.
predict
(self, X)Predict class labels for samples in X.
predict_log_proba
(self, X)Predict logarithm of probability estimates.
predict_proba
(self, X)Probability estimates.
score
(self, X, y[, sample_weight])Return the mean accuracy on the given test data and labels.
set_params
(self, \*\*params)Set the parameters of this estimator.
sparsify
(self)Convert coefficient matrix to sparse format.

__init__
(self, penalty='l2', dual=False, tol=0.0001, C=1.0, fit_intercept=True, intercept_scaling=1, class_weight=None, random_state=None, solver='lbfgs', max_iter=100, multi_class='auto', verbose=0, warm_start=False, n_jobs=None, l1_ratio=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.

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

densify
(self)[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
Fitted estimator.

fit
(self, X, y, sample_weight=None)[source]¶ Fit the model according to the given training data.
 Parameters
 X{arraylike, 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.
 yarraylike of shape (n_samples,)
Target vector relative to X.
 sample_weightarraylike 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.
New in version 0.17: sample_weight support to LogisticRegression.
 Returns
 self
Fitted estimator.
Notes
The SAGA solver supports both float64 and float32 bit arrays.

get_params
(self, deep=True)[source]¶ 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
 paramsmapping of string to any
Parameter names mapped to their values.

predict
(self, X)[source]¶ Predict class labels for samples in X.
 Parameters
 Xarray_like or sparse matrix, shape (n_samples, n_features)
Samples.
 Returns
 Carray, shape [n_samples]
Predicted class label per sample.

predict_log_proba
(self, X)[source]¶ Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Vector to be scored, where
n_samples
is the number of samples andn_features
is the number of features.
 Returns
 Tarraylike of 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
(self, 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
 Xarraylike of shape (n_samples, n_features)
Vector to be scored, where
n_samples
is the number of samples andn_features
is the number of features.
 Returns
 Tarraylike 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
(self, X, y, sample_weight=None)[source]¶ Return 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
 Xarraylike of shape (n_samples, n_features)
Test samples.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True labels for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
Mean accuracy of self.predict(X) wrt. y.

set_params
(self, **params)[source]¶ 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
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.

sparsify
(self)[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
Fitted 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.