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# `sklearn.linear_model`.Lars

class sklearn.linear_model.Lars(*, fit_intercept=True, verbose=False, normalize='deprecated', precompute='auto', n_nonzero_coefs=500, eps=2.220446049250313e-16, copy_X=True, fit_path=True, jitter=None, random_state=None)

  Least Angle Regression model a.k.a. LAR.

  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.

    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.

    n_nonzero_coefs int, default=500

      Target number of non-zero coefficients. Use `np.inf` for no limit.

    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.

    fit_path bool, default=True

      If True the full path is stored in the `coef_path_` attribute. If you compute the solution for a large problem or many targets, setting `fit_path` to `False` will lead to a speedup, especially with a small alpha.

    jitter float, default=None

      Upper bound on a uniform noise parameter to be added to the `y` values, to satisfy the model’s assumption of one-at-a-time computations. Might help with stability.

      New in version 0.23.

    random_state int, RandomState instance or None, default=None

      Determines random number generation for jittering. Pass an int for reproducible output across multiple function calls. See Glossary. Ignored if `jitter` is None.

      New in version 0.23.

  Attributes:
    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 this is a list of array-like, the length of the outer list is `n_targets`.

    active_list of shape (n_alphas,) or list of such lists

      Indices of active variables at the end of the path. If this is a list of list, the length of the outer list is `n_targets`.

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

      The varying values of the coefficients along the path. It is not present if the `fit_path` parameter is `False`. If this is a list of array-like, the length of the outer list is `n_targets`.

    coef_array-like of shape (n_features,) or (n_targets, n_features)

      Parameter vector (w in the formulation formula).

    intercept_float or array-like of shape (n_targets,)

      Independent term in decision function.

    n_iter_array-like or int

      The number of iterations taken by lars_path to find the grid of alphas for each target.

    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.

  `LarsCV`

    Cross-validated Least Angle Regression model.

  `sklearn.decomposition.sparse_encode`

    Sparse coding.

  Examples

      >>> from sklearn import linear_model
      >>> reg = linear_model.Lars(n_nonzero_coefs=1)
      >>> reg.fit([[-1, 1], [0, 0], [1, 1]], [-1.1111, 0, -1.1111])
      Lars(n_nonzero_coefs=1)
      >>> print(reg.coef_)
      [ 0. -1.11...]

  Methods

  `fit`(X, y[, Xy]) | 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, Xy=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,) or (n_samples, n_targets)

        Target values.

      Xy array-like of shape (n_features,) or (n_features, n_targets), default=None

        Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

    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 = '$UNCHANGED$') → Lars

    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 = '$UNCHANGED$') → Lars

    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.