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# `sklearn.linear_model`.LassoLarsIC

class sklearn.linear_model.LassoLarsIC(criterion='aic', *, fit_intercept=True, verbose=False, normalize='deprecated', precompute='auto', max_iter=500, eps=2.220446049250313e-16, copy_X=True, positive=False, noise_variance=None)

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

  The optimization objective for Lasso is:

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

  AIC is the Akaike information criterion [2] and BIC is the Bayes Information criterion [3]. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.

  Read more in the User Guide.

  Parameters:
    criterion{‘aic’, ‘bic’}, default=’aic’

      The type of criterion to use.

    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.

    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, ‘auto’ or array-like, default=’auto’

      Whether to use a precomputed Gram matrix to speed up calculations. If set to `'auto'` let us decide. The Gram matrix can also be passed as argument.

    max_iter int, default=500

      Maximum number of iterations to perform. Can be used for early stopping.

    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 LassoLarsIC only makes sense for problems where a sparse solution is expected and/or reached.

    noise_variance float, default=None

      The estimated noise variance of the data. If `None`, an unbiased estimate is computed by an OLS model. However, it is only possible in the case where `n_samples > n_features + fit_intercept`.

      New in version 1.1.

  Attributes:
    coef_array-like of shape (n_features,)

      parameter vector (w in the formulation formula)

    intercept_float

      independent term in decision function.

    alpha_float

      the alpha parameter chosen by the information criterion

    alphas_array-like of shape (n_alphas + 1,) or list of such arrays

      Maximum of covariances (in absolute value) at each iteration. `n_alphas` is either `max_iter`, `n_features` or the number of nodes in the path with `alpha >= alpha_min`, whichever is smaller. If a list, it will be of length `n_targets`.

    n_iter_int

      number of iterations run by lars_path to find the grid of alphas.

    criterion_array-like of shape (n_alphas,)

      The value of the information criteria (‘aic’, ‘bic’) across all alphas. The alpha which has the smallest information criterion is chosen, as specified in [1].

    noise_variance_float

      The estimated noise variance from the data used to compute the criterion.

      New in version 1.1.

    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.

  `LassoLarsCV`

    Cross-validated Lasso, using the LARS algorithm.

  `sklearn.decomposition.sparse_encode`

    Sparse coding.

  Notes

  The number of degrees of freedom is computed as in [1].

  To have more details regarding the mathematical formulation of the AIC and BIC criteria, please refer to User Guide.

  References

  [1] (1,2)

  Zou, Hui, Trevor Hastie, and Robert Tibshirani. “On the degrees of freedom of the lasso.” The Annals of Statistics 35.5 (2007): 2173-2192.

  [2]

  Wikipedia entry on the Akaike information criterion

  [3]

  Wikipedia entry on the Bayesian information criterion

  Examples

      >>> from sklearn import linear_model
      >>> reg = linear_model.LassoLarsIC(criterion='bic')
      >>> X = [[-2, 2], [-1, 1], [0, 0], [1, 1], [2, 2]]
      >>> y = [-2.2222, -1.1111, 0, -1.1111, -2.2222]
      >>> reg.fit(X, y)
      LassoLarsIC(criterion='bic')
      >>> print(reg.coef_)
      [ 0.  -1.11...]

  Methods

  `fit`(X, y[, copy_X]) | 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`(*[, copy_X]) | 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, copy_X=None)

    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. Will be cast to X’s dtype if necessary.

      copy_X bool, default=None

        If provided, this parameter will override the choice of copy_X made at instance creation. If `True`, X will be copied; else, it may be overwritten.

    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(*, copy_X: bool | None | str = '$UNCHANGED$') → LassoLarsIC

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

        Metadata routing for `copy_X` 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 = '$UNCHANGED$') → LassoLarsIC

    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.LassoLarsIC`

Lasso model selection via information criteria

Lasso model selection via information criteria

Lasso model selection: AIC-BIC / cross-validation

Lasso model selection: AIC-BIC / cross-validation