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# `sklearn.linear_model`.HuberRegressor

class sklearn.linear_model.HuberRegressor(*, epsilon=1.35, max_iter=100, alpha=0.0001, warm_start=False, fit_intercept=True, tol=1e-05)

  L2-regularized linear regression model that is robust to outliers.

  The Huber Regressor optimizes the squared loss for the samples where `|(y - Xw - c) / sigma| < epsilon` and the absolute loss for the samples where `|(y - Xw - c) / sigma| > epsilon`, where the model coefficients `w`, the intercept `c` and the scale `sigma` are parameters to be optimized. The parameter sigma makes sure that if y is scaled up or down by a certain factor, one does not need to rescale epsilon to achieve the same robustness. Note that this does not take into account the fact that the different features of X may be of different scales.

  The Huber loss function has the advantage of not being heavily influenced by the outliers while not completely ignoring their effect.

  Read more in the User Guide

  New in version 0.18.

  Parameters:
    epsilon float, default=1.35

      The parameter epsilon controls the number of samples that should be classified as outliers. The smaller the epsilon, the more robust it is to outliers. Epsilon must be in the range `[1, inf)`.

    max_iter int, default=100

      Maximum number of iterations that `scipy.optimize.minimize(method="L-BFGS-B")` should run for.

    alpha float, default=0.0001

      Strength of the squared L2 regularization. Note that the penalty is equal to `alpha * ||w||^2`. Must be in the range `[0, inf)`.

    warm_start bool, default=False

      This is useful if the stored attributes of a previously used model has to be reused. If set to False, then the coefficients will be rewritten for every call to fit. See the Glossary.

    fit_intercept bool, default=True

      Whether or not to fit the intercept. This can be set to False if the data is already centered around the origin.

    tol float, default=1e-05

      The iteration will stop when `max{|proj g_i | i = 1, ..., n}` <= `tol` where pg_i is the i-th component of the projected gradient.

  Attributes:
    coef_array, shape (n_features,)

      Features got by optimizing the L2-regularized Huber loss.

    intercept_float

      Bias.

    scale_float

      The value by which `|y - Xw - c|` is scaled down.

    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.

    n_iter_int

      Number of iterations that `scipy.optimize.minimize(method="L-BFGS-B")` has run for.

      Changed in version 0.20: In SciPy <= 1.0.0 the number of lbfgs iterations may exceed `max_iter`. `n_iter_` will now report at most `max_iter`.

    outliers_array, shape (n_samples,)

      A boolean mask which is set to True where the samples are identified as outliers.

  See also

  `RANSACRegressor`

    RANSAC (RANdom SAmple Consensus) algorithm.

  `TheilSenRegressor`

    Theil-Sen Estimator robust multivariate regression model.

  `SGDRegressor`

    Fitted by minimizing a regularized empirical loss with SGD.

  References

  [1]

  Peter J. Huber, Elvezio M. Ronchetti, Robust Statistics Concomitant scale estimates, pg 172

  [2]

  Art B. Owen (2006), A robust hybrid of lasso and ridge regression. https://statweb.stanford.edu/~owen/reports/hhu.pdf

  Examples

      >>> import numpy as np
      >>> from sklearn.linear_model import HuberRegressor, LinearRegression
      >>> from sklearn.datasets import make_regression
      >>> rng = np.random.RandomState(0)
      >>> X, y, coef = make_regression(
      ...     n_samples=200, n_features=2, noise=4.0, coef=True, random_state=0)
      >>> X[:4] = rng.uniform(10, 20, (4, 2))
      >>> y[:4] = rng.uniform(10, 20, 4)
      >>> huber = HuberRegressor().fit(X, y)
      >>> huber.score(X, y)
      -7.284...
      >>> huber.predict(X[:1,])
      array([806.7200...])
      >>> linear = LinearRegression().fit(X, y)
      >>> print("True coefficients:", coef)
      True coefficients: [20.4923...  34.1698...]
      >>> print("Huber coefficients:", huber.coef_)
      Huber coefficients: [17.7906... 31.0106...]
      >>> print("Linear Regression coefficients:", linear.coef_)
      Linear Regression coefficients: [-1.9221...  7.0226...]

  Methods

  `fit`(X, y[, sample_weight]) | Fit the model according to the given 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`(*[, 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)

    Fit the model according to the given training data.

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

        Training vector, where `n_samples` is the number of samples and `n_features` is the number of features.

      y array-like, shape (n_samples,)

        Target vector relative to X.

      sample_weight array-like, shape (n_samples,)

        Weight given to each sample.

    Returns:
      self object

        Fitted `HuberRegressor` estimator.

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

    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:
      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 = '$UNCHANGED$') → HuberRegressor

    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.HuberRegressor`

HuberRegressor vs Ridge on dataset with strong outliers

HuberRegressor vs Ridge on dataset with strong outliers

Ridge coefficients as a function of the L2 Regularization

Ridge coefficients as a function of the L2 Regularization

Robust linear estimator fitting

Robust linear estimator fitting