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# `sklearn.linear_model`.lasso_path

sklearn.linear_model.lasso_path(X, y, *, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, **params)

  Compute Lasso path with coordinate descent.

  The Lasso optimization function varies for mono and multi-outputs.

  For mono-output tasks it is:

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

  For multi-output tasks it is:

      (1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21

  Where:

      ||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

  i.e. the sum of norm of each row.

  Read more in the User Guide.

  Parameters:
    X{array-like, sparse matrix} of shape (n_samples, n_features)

      Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If `y` is mono-output then `X` can be sparse.

    y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)

      Target values.

    eps float, default=1e-3

      Length of the path. `eps=1e-3` means that `alpha_min / alpha_max = 1e-3`.

    n_alphas int, default=100

      Number of alphas along the regularization path.

    alphas ndarray, default=None

      List of alphas where to compute the models. If `None` alphas are set automatically.

    precompute‘auto’, bool or array-like of shape (n_features, n_features), 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.

    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.

    copy_X bool, default=True

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

    coef_init ndarray of shape (n_features, ), default=None

      The initial values of the coefficients.

    verbose bool or int, default=False

      Amount of verbosity.

    return_n_iter bool, default=False

      Whether to return the number of iterations or not.

    positive bool, default=False

      If set to True, forces coefficients to be positive. (Only allowed when `y.ndim == 1`).

    **params kwargs

      Keyword arguments passed to the coordinate descent solver.

  Returns:
    alphas ndarray of shape (n_alphas,)

      The alphas along the path where models are computed.

    coefs ndarray of shape (n_features, n_alphas) or (n_targets, n_features, n_alphas)

      Coefficients along the path.

    dual_gaps ndarray of shape (n_alphas,)

      The dual gaps at the end of the optimization for each alpha.

    n_iters list of int

      The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.

  See also

  `lars_path`

    Compute Least Angle Regression or Lasso path using LARS algorithm.

  `Lasso`

    The Lasso is a linear model that estimates sparse coefficients.

  `LassoLars`

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

  `LassoCV`

    Lasso linear model with iterative fitting along a regularization path.

  `LassoLarsCV`

    Cross-validated Lasso using the LARS algorithm.

  `sklearn.decomposition.sparse_encode`

    Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

  Notes

  For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

  To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

  Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path

  Examples

  Comparing lasso_path and lars_path with interpolation:

      >>> import numpy as np
      >>> from sklearn.linear_model import lasso_path
      >>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T
      >>> y = np.array([1, 2, 3.1])
      >>> # Use lasso_path to compute a coefficient path
      >>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5])
      >>> print(coef_path)
      [[0.         0.         0.46874778]
       [0.2159048  0.4425765  0.23689075]]

      >>> # Now use lars_path and 1D linear interpolation to compute the
      >>> # same path
      >>> from sklearn.linear_model import lars_path
      >>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso')
      >>> from scipy import interpolate
      >>> coef_path_continuous = interpolate.interp1d(alphas[::-1],
      ...                                             coef_path_lars[:, ::-1])
      >>> print(coef_path_continuous([5., 1., .5]))
      [[0.         0.         0.46915237]
       [0.2159048  0.4425765  0.23668876]]

## Examples using `sklearn.linear_model.lasso_path`

Lasso and Elastic Net

Lasso and Elastic Net