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# `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=None, verbose=0, refit=True, intercept_scaling=1.0, multi_class='auto', random_state=None, l1_ratios=None)

  Logistic Regression CV (aka logit, MaxEnt) classifier.

  See glossary entry for cross-validation estimator.

  This class implements logistic regression using liblinear, newton-cg, sag of lbfgs optimizer. The newton-cg, 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. Elastic-Net penalty is only supported by the saga solver.

  For the grid of `Cs` values and `l1_ratios` values, the best hyperparameter is selected by the cross-validator `StratifiedKFold`, but it can be changed using the cv parameter. The ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers can warm-start the coefficients (see Glossary).

  Read more in the User Guide.

  Parameters:
    Cs int or list of floats, default=10

      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 1e-4 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.

    cv int 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 module `sklearn.model_selection` module for the list of possible cross-validation objects.

      Changed in version 0.22: `cv` default value if None changed from 3-fold to 5-fold.

    dual bool, default=False

      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.

    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 parameter `solver` below, to know the compatibility between the penalty and solver.

    scoring str or callable, default=None

      A string (see model evaluation documentation) or a scorer callable object / function with signature `scorer(estimator, X, y)`. For a list of scoring functions that can be used, look at `sklearn.metrics`. The default scoring option used is ‘accuracy’.

    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, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss;

      > - ‘liblinear’ might be slower in `LogisticRegressionCV` because it does not handle warm-starting. ‘liblinear’ is limited to one-versus-rest schemes.

      > - ‘newton-cholesky’ is a good choice for `n_samples` >> `n_features`, especially with one-hot encoded categorical features with rare categories. Note that it is limited to binary classification and the one-versus-rest reduction for multiclass classification. Be aware that the memory usage of this solver has a quadratic dependency on `n_features` because it explicitly computes the Hessian matrix.

      Warning

      The choice of the algorithm depends on the penalty chosen. Supported penalties by solver:

      - ‘lbfgs’ - [‘l2’]

      - ‘liblinear’ - [‘l1’, ‘l2’]

      - ‘newton-cg’ - [‘l2’]

      - ‘newton-cholesky’ - [‘l2’]

      - ‘sag’ - [‘l2’]

      - ‘saga’ - [‘elasticnet’, ‘l1’, ‘l2’]

      Note

      ‘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.

      New in version 1.2: newton-cholesky solver.

    tol float, default=1e-4

      Tolerance for stopping criteria.

    max_iter int, default=100

      Maximum number of iterations of the optimization algorithm.

    class_weight dict 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’

    n_jobs int, default=None

      Number of CPU cores used during the cross-validation loop. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    verbose int, default=0

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

    refit bool, default=True

      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.

    intercept_scaling float, 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.

    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.

    random_state int, RandomState instance, default=None

      Used when `solver='sag'`, ‘saga’ or ‘liblinear’ to shuffle the data. Note that this only applies to the solver and not the cross-validation generator. See Glossary for details.

    l1_ratios list of float, default=None

      The list of Elastic-Net mixing parameter, with `0 <= l1_ratio <= 1`. Only used if `penalty='elasticnet'`. A value of 0 is equivalent to using `penalty='l2'`, while 1 is equivalent to using `penalty='l1'`. For `0 < 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.

    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 problem is binary.

    Cs_ndarray of shape (n_cs)

      Array of C i.e. inverse of regularization parameter values used for 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 obtained during cross-validating 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, n_cs, n_features)` or `(n_folds, n_cs, n_features + 1)` depending on whether the intercept is fit or not. If `penalty='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 the grid of scores obtained during cross-validating 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, n_cs)` or `(n_folds, n_cs, n_l1_ratios)` if `penalty='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 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. `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. If refit is set to False, then for each class, the best l1_ratio is the average of the l1_ratio’s that correspond to the best scores for each fold. `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. If `penalty='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 during fit.

      New in version 0.24.

    feature_names_in_ndarray of shape (`n_features_in_`,)

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

      New in version 1.0.

  See also

  `LogisticRegression`

    Logistic regression without tuning the hyperparameter `C`.

  Examples

      >>> from sklearn.datasets import load_iris
      >>> from sklearn.linear_model import LogisticRegressionCV
      >>> 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...

  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.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `predict`(X) | Predict class labels for samples in X.
  `predict_log_proba`(X) | Predict logarithm of probability estimates.
  `predict_proba`(X) | Probability estimates.
  `score`(X, y[, sample_weight]) | Score using the `scoring` option on the given test data and labels.
  `set_fit_request`(*[, sample_weight]) | Request metadata passed to the `fit` method.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.
  `sparsify`() | Convert coefficient matrix to sparse format.

  decision_function(X)

    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:
      scores ndarray 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()

    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)

    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.

      y array-like of shape (n_samples,)

        Target vector relative to X.

      sample_weight array-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.

    Returns:
      self object

        Fitted LogisticRegressionCV estimator.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

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

    Returns:
      params dict

        Parameter names mapped to their values.

  predict(X)

    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_pred ndarray of shape (n_samples,)

        Vector containing the class labels for each sample.

  predict_log_proba(X)

    Predict logarithm of probability estimates.

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

    Parameters:
      X array-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:
      T array-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)

    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:
      X array-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:
      T array-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)

    Score using the `scoring` option on the given test data and labels.

    Parameters:
      X array-like of shape (n_samples, n_features)

        Test samples.

      y array-like of shape (n_samples,)

        True labels for X.

      sample_weight array-like of shape (n_samples,), default=None

        Sample weights.

    Returns:
      score float

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

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

    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.

    New in version 1.3.

    Note

    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_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `fit`.

    Returns:
      self object

        The updated object.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

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

    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.

    New in version 1.3.

    Note

    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_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `score`.

    Returns:
      self object

        The updated object.

  sparsify()

    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.

## Examples using `sklearn.linear_model.LogisticRegressionCV`

Importance of Feature Scaling

Importance of Feature Scaling