Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

# `sklearn.linear_model`.Lasso

class sklearn.linear_model.Lasso(alpha=1.0, *, fit_intercept=True, precompute=False, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')

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

  The optimization objective for Lasso is:

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

  Technically the Lasso model is optimizing the same objective function as the Elastic Net with `l1_ratio=1.0` (no L2 penalty).

  Read more in the User Guide.

  Parameters:
    alpha float, default=1.0

      Constant that multiplies the L1 term, controlling regularization strength. `alpha` must be a non-negative float i.e. in `[0, inf)`.

      When `alpha = 0`, the objective is equivalent to ordinary least squares, solved by the `LinearRegression` object. For numerical reasons, using `alpha = 0` with the `Lasso` object is not advised. Instead, you should use the `LinearRegression` object.

    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).

    precompute bool or array-like of shape (n_features, n_features), default=False

      Whether to use a precomputed Gram matrix to speed up calculations. The Gram matrix can also be passed as argument. For sparse input this option is always `False` to preserve sparsity.

    copy_X bool, default=True

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

    max_iter int, default=1000

      The maximum number of iterations.

    tol float, default=1e-4

      The tolerance for the optimization: if the updates are smaller than `tol`, the optimization code checks the dual gap for optimality and continues until it is smaller than `tol`, see Notes below.

    warm_start bool, default=False

      When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.

    positive bool, default=False

      When set to `True`, forces the coefficients to be positive.

    random_state int, RandomState instance, default=None

      The seed of the pseudo random number generator that selects a random feature to update. Used when `selection` == ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary.

    selection{‘cyclic’, ‘random’}, default=’cyclic’

      If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

  Attributes:
    coef_ndarray of shape (n_features,) or (n_targets, n_features)

      Parameter vector (w in the cost function formula).

    dual_gap_float or ndarray of shape (n_targets,)

      Given param alpha, the dual gaps at the end of the optimization, same shape as each observation of y.

    `sparse_coef_`sparse matrix of shape (n_features, 1) or (n_targets, n_features)

      Sparse representation of the fitted `coef_`.

    intercept_float or ndarray of shape (n_targets,)

      Independent term in decision function.

    n_iter_int or list of int

      Number of iterations run by the coordinate descent solver to reach the specified tolerance.

    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`

    Regularization path using LARS.

  `lasso_path`

    Regularization path using Lasso.

  `LassoLars`

    Lasso Path along the regularization parameter using LARS algorithm.

  `LassoCV`

    Lasso alpha parameter by cross-validation.

  `LassoLarsCV`

    Lasso least angle parameter algorithm by cross-validation.

  `sklearn.decomposition.sparse_encode`

    Sparse coding array estimator.

  Notes

  The algorithm used to fit the model is coordinate descent.

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

  Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to `1 / (2C)` in other linear models such as `LogisticRegression` or `LinearSVC`. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.

  The precise stopping criteria based on `tol` are the following: First, check that that maximum coordinate update, i.e. \(\max_j |w_j^{new} - w_j^{old}|\) is smaller than `tol` times the maximum absolute coefficient, \(\max_j |w_j|\). If so, then additionally check whether the dual gap is smaller than `tol` times \(||y||_2^2 / n_{\text{samples}}\).

  The target can be a 2-dimensional array, resulting in the optimization of the following objective:

      (1 / (2 * n_samples)) * ||Y - XW||^2_F + alpha * ||W||_11

  where \(||W||_{1,1}\) is the sum of the magnitude of the matrix coefficients. It should not be confused with `MultiTaskLasso` which instead penalizes the \(L_{2,1}\) norm of the coefficients, yielding row-wise sparsity in the coefficients.

  Examples

      >>> from sklearn import linear_model
      >>> clf = linear_model.Lasso(alpha=0.1)
      >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
      Lasso(alpha=0.1)
      >>> print(clf.coef_)
      [0.85 0.  ]
      >>> print(clf.intercept_)
      0.15...

  Methods

  `fit`(X, y[, sample_weight, check_input]) | Fit model with coordinate descent.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `path`(X, y, *[, l1_ratio, eps, n_alphas, ...]) | Compute elastic net path with coordinate descent.
  `predict`(X) | Predict using the linear model.
  `score`(X, y[, sample_weight]) | Return the coefficient of determination of the prediction.
  `set_fit_request`(*[, check_input, 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.

  fit(X, y, sample_weight=None, check_input=True)

    Fit model with coordinate descent.

    Parameters:
      X{ndarray, sparse matrix} of (n_samples, n_features)

        Data.

      y ndarray of shape (n_samples,) or (n_samples, n_targets)

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

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

        Sample weights. Internally, the `sample_weight` vector will be rescaled to sum to `n_samples`.

        New in version 0.23.

      check_input bool, default=True

        Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

    Returns:
      self object

        Fitted estimator.

    Notes

    Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortran-contiguous numpy array if necessary.

    To avoid memory re-allocation it is advised to allocate the initial data in memory directly using that format.

  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.

  static path(X, y, *, l1_ratio=0.5, 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, check_input=True, **params)

    Compute elastic net path with coordinate descent.

    The elastic net optimization function varies for mono and multi-outputs.

    For mono-output tasks it is:

        1 / (2 * n_samples) * ||y - Xw||^2_2
        + alpha * l1_ratio * ||w||_1
        + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2

    For multi-output tasks it is:

        (1 / (2 * n_samples)) * ||Y - XW||_Fro^2
        + alpha * l1_ratio * ||W||_21
        + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2

    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.

      l1_ratio float, default=0.5

        Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). `l1_ratio=1` corresponds to the Lasso.

      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`).

      check_input bool, default=True

        If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.

      **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. (Is returned when `return_n_iter` is set to True).

    See also

    `MultiTaskElasticNet`

      Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.

    `MultiTaskElasticNetCV`

      Multi-task L1/L2 ElasticNet with built-in cross-validation.

    `ElasticNet`

      Linear regression with combined L1 and L2 priors as regularizer.

    `ElasticNetCV`

      Elastic Net model with iterative fitting along a regularization path.

    Notes

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

  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(*, check_input: bool | None | str = '$UNCHANGED$', sample_weight: bool | None | str = '$UNCHANGED$') → Lasso

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

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

      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 = '$UNCHANGED$') → Lasso

    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.

  property sparse_coef_

    Sparse representation of the fitted `coef_`.

## Examples using `sklearn.linear_model.Lasso`

Release Highlights for scikit-learn 0.23

Release Highlights for scikit-learn 0.23

Compressive sensing: tomography reconstruction with L1 prior (Lasso)

Compressive sensing: tomography reconstruction with L1 prior (Lasso)

Joint feature selection with multi-task Lasso

Joint feature selection with multi-task Lasso

L1-based models for Sparse Signals

L1-based models for Sparse Signals

Lasso on dense and sparse data

Lasso on dense and sparse data

Cross-validation on diabetes Dataset Exercise

Cross-validation on diabetes Dataset Exercise