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# `sklearn.linear_model`.LassoLarsCV

class sklearn.linear_model.LassoLarsCV(*, fit_intercept=True, verbose=False, max_iter=500, normalize='deprecated', precompute='auto', cv=None, max_n_alphas=1000, n_jobs=None, eps=2.220446049250313e-16, copy_X=True, positive=False)

  Cross-validated Lasso, using the LARS algorithm.

  See glossary entry for cross-validation estimator.

  The optimization objective for Lasso is:

      (1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

  Read more in the User Guide.

  Parameters:
    fit_intercept bool, default=True

      Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).

    verbose bool or int, default=False

      Sets the verbosity amount.

    max_iter int, default=500

      Maximum number of iterations to perform.

    normalize bool, default=False

      This parameter is ignored when `fit_intercept` is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use `StandardScaler` before calling `fit` on an estimator with `normalize=False`.

      Changed in version 1.2: default changed from True to False in 1.2.

      Deprecated since version 1.2: `normalize` was deprecated in version 1.2 and will be removed in 1.4.

    precompute bool or ‘auto’ , default=’auto’

      Whether to use a precomputed Gram matrix to speed up calculations. If set to `'auto'` let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X.

    cv int, cross-validation generator or an iterable, default=None

      Determines the cross-validation splitting strategy. Possible inputs for cv are:

      - None, to use the default 5-fold cross-validation,

      - integer, to specify the number of folds.

      - CV splitter,

      - An iterable yielding (train, test) splits as arrays of indices.

      For integer/None inputs, `KFold` is used.

      Refer User Guide for the various cross-validation strategies that can be used here.

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

    max_n_alphas int, default=1000

      The maximum number of points on the path used to compute the residuals in the cross-validation.

    n_jobs int or None, default=None

      Number of CPUs to use during the cross validation. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    eps float, default=np.finfo(float).eps

      The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the `tol` parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.

    copy_X bool, default=True

      If True, X will be copied; else, it may be overwritten.

    positive bool, default=False

      Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (`alphas_[alphas_ > 0.].min()` when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsCV only makes sense for problems where a sparse solution is expected and/or reached.

  Attributes:
    coef_array-like of shape (n_features,)

      parameter vector (w in the formulation formula)

    intercept_float

      independent term in decision function.

    coef_path_array-like of shape (n_features, n_alphas)

      the varying values of the coefficients along the path

    alpha_float

      the estimated regularization parameter alpha

    alphas_array-like of shape (n_alphas,)

      the different values of alpha along the path

    cv_alphas_array-like of shape (n_cv_alphas,)

      all the values of alpha along the path for the different folds

    mse_path_array-like of shape (n_folds, n_cv_alphas)

      the mean square error on left-out for each fold along the path (alpha values given by `cv_alphas`)

    n_iter_array-like or int

      the number of iterations run by Lars with the optimal alpha.

    active_list of int

      Indices of active variables at the end of the path.

    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

  `lars_path`

    Compute Least Angle Regression or Lasso path using LARS algorithm.

  `lasso_path`

    Compute Lasso path with coordinate descent.

  `Lasso`

    Linear Model trained with L1 prior as regularizer (aka the Lasso).

  `LassoCV`

    Lasso linear model with iterative fitting along a regularization path.

  `LassoLars`

    Lasso model fit with Least Angle Regression a.k.a. Lars.

  `LassoLarsIC`

    Lasso model fit with Lars using BIC or AIC for model selection.

  `sklearn.decomposition.sparse_encode`

    Sparse coding.

  Notes

  The object solves the same problem as the `LassoCV` object. However, unlike the `LassoCV`, it find the relevant alphas values by itself. In general, because of this property, it will be more stable. However, it is more fragile to heavily multicollinear datasets.

  It is more efficient than the `LassoCV` if only a small number of features are selected compared to the total number, for instance if there are very few samples compared to the number of features.

  In `fit`, once the best parameter `alpha` is found through cross-validation, the model is fit again using the entire training set.

  Examples

      >>> from sklearn.linear_model import LassoLarsCV
      >>> from sklearn.datasets import make_regression
      >>> X, y = make_regression(noise=4.0, random_state=0)
      >>> reg = LassoLarsCV(cv=5).fit(X, y)
      >>> reg.score(X, y)
      0.9993...
      >>> reg.alpha_
      0.3972...
      >>> reg.predict(X[:1,])
      array([-78.4831...])

  Methods

  `fit`(X, y) | Fit the model using X, y as training data.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `predict`(X) | Predict using the linear model.
  `score`(X, y[, sample_weight]) | Return the coefficient of determination of the prediction.
  `set_fit_request`(*[, Xy]) | 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.

  fit(X, y)

    Fit the model using X, y as training data.

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

        Training data.

      y array-like of shape (n_samples,)

        Target values.

    Returns:
      self object

        Returns an instance of self.

  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 using the linear model.

    Parameters:
      X array-like or sparse matrix, shape (n_samples, n_features)

        Samples.

    Returns:
      C array, shape (n_samples,)

        Returns predicted values.

  score(X, y, sample_weight=None)

    Return the coefficient of determination of the prediction.

    The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares `((y_true - y_pred)** 2).sum()` and \(v\) is the total sum of squares `((y_true - y_true.mean()) ** 2).sum()`. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of `y`, disregarding the input features, would get a \(R^2\) score of 0.0.

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

        Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape `(n_samples, n_samples_fitted)`, where `n_samples_fitted` is the number of samples used in the fitting for the estimator.

      y array-like of shape (n_samples,) or (n_samples, n_outputs)

        True values for `X`.

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

        Sample weights.

    Returns:
      score float

        \(R^2\) of `self.predict(X)` w.r.t. `y`.

    Notes

    The \(R^2\) score used when calling `score` on a regressor uses `multioutput='uniform_average'` from version 0.23 to keep consistent with default value of `r2_score`. This influences the `score` method of all the multioutput regressors (except for `MultiOutputRegressor`).

  set_fit_request(*, Xy: bool | None | str = '$UNCHANGED$') → LassoLarsCV

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

        Metadata routing for `Xy` 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 = '$UNCHANGED$') → LassoLarsCV

    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.

## Examples using `sklearn.linear_model.LassoLarsCV`

Lasso model selection: AIC-BIC / cross-validation

Lasso model selection: AIC-BIC / cross-validation