Logistic Regression (aka logit, MaxEnt) classifier.

This class implements regularized logistic regression using the ‘liblinear’ library, ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers. Note that regularization is applied by default . 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).

The ‘newton-cg’, ‘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 Elastic-Net regularization is only supported by the ‘saga’ solver.

For multiclass problems, all solvers but ‘liblinear’ optimize the (penalized) multinomial loss. ‘liblinear’ only handle binary classification but can be extended to handle multiclass by using OneVsRestClassifier .

Read more in the User Guide .

Specify the norm of the penalty:

Warning

Some penalties may not work with some solvers. See the parameter solver below, to know the compatibility between the penalty and solver.

Added in version 0.19: l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)

Dual (constrained) or primal (regularized, see also this equation ) formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.

Tolerance for stopping criteria.

Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.

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

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.

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.

Added in version 0.17: class_weight=’balanced’

Used when solver == ‘sag’, ‘saga’ or ‘liblinear’ to shuffle the data. See Glossary for details.

Algorithm to use in the optimization problem. Default is ‘lbfgs’. To choose a solver, you might want to consider the following aspects:

Warning

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

solver

penalty

multinomial multiclass

‘lbfgs’

‘l2’, None

‘liblinear’

‘l1’, ‘l2’

‘newton-cg’

‘l2’, None

‘newton-cholesky’

‘l2’, None

‘sag’

‘l2’, None

‘saga’

‘elasticnet’, ‘l1’, ‘l2’, None

‘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 .

See also

Refer to the User Guide for more information regarding LogisticRegression and more specifically the Table summarizing solver/penalty supports.

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

Added in version 0.19: SAGA solver.

Changed in version 0.22: The default solver changed from ‘liblinear’ to ‘lbfgs’ in 0.22.

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

Maximum number of iterations taken for the solvers to converge.

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’.

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 1.7. From then on, the recommended ‘multinomial’ will always be used for n_classes >= 3 . Solvers that do not support ‘multinomial’ will raise an error. Use sklearn.multiclass.OneVsRestClassifier(LogisticRegression()) if you still want to use OvR.

For the liblinear and lbfgs solvers set verbose to any positive number for verbosity.

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 .

Added in version 0.17: warm_start to support lbfgs , newton-cg , sag , saga solvers.

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 a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

The Elastic-Net mixing parameter, with 0 <= l1_ratio <= 1 . Only used if penalty='elasticnet' . Setting l1_ratio=0 is equivalent to using penalty='l2' , while setting l1_ratio=1 is equivalent to using penalty='l1' . For 0 < l1_ratio <1 , the penalty is a combination of L1 and L2.

A list of class labels known to the classifier.

Coefficient of the features in the decision function.

coef_ is of shape (1, n_features) when the given problem is binary. In particular, when multi_class='multinomial' , coef_ corresponds to outcome 1 (True) and -coef_ corresponds to outcome 0 (False).

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, when multi_class='multinomial' , intercept_ corresponds to outcome 1 (True) and -intercept_ corresponds to outcome 0 (False).

Number of features seen during fit .

Added in version 0.24.

Names of features seen during fit . Defined only when X has feature names that are all strings.

Added in version 1.0.

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 most max_iter .

See also

Incrementally trained logistic regression (when given the parameter loss="log_loss" ).

Logistic regression with built-in 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

Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html

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

Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal-00860051/document

“SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives”

methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. 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([[9.82e-01, 1.82e-02, 1.44e-08],
       [9.72e-01, 2.82e-02, 3.02e-08]])
>>> clf.score(X, y)
For a comparison of the LogisticRegression with other classifiers see:
Plot classification probability.
decision_function(X)[source]#
Predict confidence scores for samples.
The confidence score for a sample is proportional to the signed
distance 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 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 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(X, y, sample_weight=None)[source]#
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.
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.
Added in version 0.17: sample_weight support to LogisticRegression.
get_metadata_routing()[source]#
Get metadata routing of this object.
Please check User Guide on how the routing
mechanism works.
Returns:
routingMetadataRequest
A MetadataRequest encapsulating
routing information.
Parameters:
deepbool, default=True
If True, will return the parameters for this estimator and
contained subobjects that are estimators.
Returns:
paramsdict
Parameter names mapped to their values.
predict_log_proba(X)[source]#
Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the
label of classes.
Parameters:
Xarray-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:
Tarray-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_.
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 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:
Xarray-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:
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 in self.classes_.
score(X, y, sample_weight=None)[source]#
Return accuracy on provided data and labels.
In multi-label 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:
Xarray-like of shape (n_samples, n_features)
Test samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)
True labels for X.
sample_weightarray-like of shape (n_samples,), default=None
Sample weights.
Returns:
scorefloat
Mean accuracy of self.predict(X) w.r.t. y.
set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → LogisticRegression[source]#
Request metadata passed to the fit method.
Note that this method is only relevant if
enable_metadata_routing=True (see sklearn.set_config).
Please see User Guide on how the routing
mechanism works.
The options for each parameter are:
True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
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 the
existing request. This allows you to change the request for some
parameters and not others.
Added in version 1.3.
This method is only relevant if this estimator is used as a
sub-estimator of a meta-estimator, e.g. used inside a
Pipeline. Otherwise it has no effect.
Parameters:
sample_weightstr, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for sample_weight parameter in fit.
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 as Pipeline). 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:
selfestimator instance
Estimator instance.
set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → LogisticRegression[source]#
Request metadata passed to the score method.
Note that this method is only relevant if
enable_metadata_routing=True (see sklearn.set_config).
Please see User Guide on how the routing
mechanism works.
The options for each parameter are:
True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
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 the
existing request. This allows you to change the request for some
parameters and not others.
Added in version 1.3.
This method is only relevant if this estimator is used as a
sub-estimator of a meta-estimator, e.g. used inside a
Pipeline. Otherwise it has no effect.
Parameters:
sample_weightstr, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for sample_weight parameter in score.
Returns:
selfobject
The updated object.
sparsify()[source]#
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.
Pipelining: chaining a PCA and a logistic regression
  
Pipelining: chaining a PCA and a logistic regression
Feature transformations with ensembles of trees
  
Feature transformations with ensembles of trees
Visualizing the probabilistic predictions of a VotingClassifier
  
Visualizing the probabilistic predictions of a VotingClassifier
Recursive feature elimination
  
Recursive feature elimination
Recursive feature elimination with cross-validation
  
Recursive feature elimination with cross-validation
Model-based and sequential feature selection
  
Model-based and sequential feature selection
Examples of Using FrozenEstimator
  
Examples of Using FrozenEstimator
Logistic function
  
Logistic function
L1 Penalty and Sparsity in Logistic Regression
  
L1 Penalty and Sparsity in Logistic Regression
Decision Boundaries of Multinomial and One-vs-Rest Logistic Regression
  
Decision Boundaries of Multinomial and One-vs-Rest Logistic Regression
Regularization path of L1- Logistic Regression
  
Regularization path of L1- Logistic Regression
Multiclass sparse logistic regression on 20newgroups
  
Multiclass sparse logistic regression on 20newgroups
MNIST classification using multinomial logistic + L1
  
MNIST classification using multinomial logistic + L1
Visualizations with Display Objects
  
Visualizations with Display Objects
Displaying estimators and complex pipelines
  
Displaying estimators and complex pipelines
Displaying Pipelines
  
Displaying Pipelines
Introducing the set_output API
  
Introducing the set_output API
Post-tuning the decision threshold for cost-sensitive learning
  
Post-tuning the decision threshold for cost-sensitive learning
Balance model complexity and cross-validated score
  
Balance model complexity and cross-validated score
Class Likelihood Ratios to measure classification performance
  
Class Likelihood Ratios to measure classification performance
Multiclass Receiver Operating Characteristic (ROC)
  
Multiclass Receiver Operating Characteristic (ROC)
Post-hoc tuning the cut-off point of decision function
  
Post-hoc tuning the cut-off point of decision function
Multilabel classification using a classifier chain
  
Multilabel classification using a classifier chain
Restricted Boltzmann Machine features for digit classification
  
Restricted Boltzmann Machine features for digit classification
Feature discretization
  
Feature discretization
Release Highlights for scikit-learn 0.22
  
Release Highlights for scikit-learn 0.22
Release Highlights for scikit-learn 0.23
  
Release Highlights for scikit-learn 0.23
Release Highlights for scikit-learn 0.24
  
Release Highlights for scikit-learn 0.24
Release Highlights for scikit-learn 1.0
  
Release Highlights for scikit-learn 1.0
Release Highlights for scikit-learn 1.1
  
Release Highlights for scikit-learn 1.1
Release Highlights for scikit-learn 1.3
  
Release Highlights for scikit-learn 1.3
Release Highlights for scikit-learn 1.5
  
Release Highlights for scikit-learn 1.5
Release Highlights for scikit-learn 1.7
  
Release Highlights for scikit-learn 1.7
Classification of text documents using sparse features
  
Classification of text documents using sparse features