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# `sklearn.linear_model`.TheilSenRegressor

class sklearn.linear_model.TheilSenRegressor(*, fit_intercept=True, copy_X=True, max_subpopulation=10000.0, n_subsamples=None, max_iter=300, tol=0.001, random_state=None, n_jobs=None, verbose=False)

  Theil-Sen Estimator: robust multivariate regression model.

  The algorithm calculates least square solutions on subsets with size n_subsamples of the samples in X. Any value of n_subsamples between the number of features and samples leads to an estimator with a compromise between robustness and efficiency. Since the number of least square solutions is “n_samples choose n_subsamples”, it can be extremely large and can therefore be limited with max_subpopulation. If this limit is reached, the subsets are chosen randomly. In a final step, the spatial median (or L1 median) is calculated of all least square solutions.

  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.

    copy_X bool, default=True

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

    max_subpopulation int, default=1e4

      Instead of computing with a set of cardinality ‘n choose k’, where n is the number of samples and k is the number of subsamples (at least number of features), consider only a stochastic subpopulation of a given maximal size if ‘n choose k’ is larger than max_subpopulation. For other than small problem sizes this parameter will determine memory usage and runtime if n_subsamples is not changed. Note that the data type should be int but floats such as 1e4 can be accepted too.

    n_subsamples int, default=None

      Number of samples to calculate the parameters. This is at least the number of features (plus 1 if fit_intercept=True) and the number of samples as a maximum. A lower number leads to a higher breakdown point and a low efficiency while a high number leads to a low breakdown point and a high efficiency. If None, take the minimum number of subsamples leading to maximal robustness. If n_subsamples is set to n_samples, Theil-Sen is identical to least squares.

    max_iter int, default=300

      Maximum number of iterations for the calculation of spatial median.

    tol float, default=1e-3

      Tolerance when calculating spatial median.

    random_state int, RandomState instance or None, default=None

      A random number generator instance to define the state of the random permutations generator. Pass an int for reproducible output across multiple function calls. See Glossary.

    n_jobs int, default=None

      Number of CPUs to use during the cross validation. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    verbose bool, default=False

      Verbose mode when fitting the model.

  Attributes:
    coef_ndarray of shape (n_features,)

      Coefficients of the regression model (median of distribution).

    intercept_float

      Estimated intercept of regression model.

    breakdown_float

      Approximated breakdown point.

    n_iter_int

      Number of iterations needed for the spatial median.

    n_subpopulation_int

      Number of combinations taken into account from ‘n choose k’, where n is the number of samples and k is the number of subsamples.

    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

  `HuberRegressor`

    Linear regression model that is robust to outliers.

  `RANSACRegressor`

    RANSAC (RANdom SAmple Consensus) algorithm.

  `SGDRegressor`

    Fitted by minimizing a regularized empirical loss with SGD.

  References

  - Theil-Sen Estimators in a Multiple Linear Regression Model, 2009 Xin Dang, Hanxiang Peng, Xueqin Wang and Heping Zhang http://home.olemiss.edu/~xdang/papers/MTSE.pdf

  Examples

      >>> from sklearn.linear_model import TheilSenRegressor
      >>> from sklearn.datasets import make_regression
      >>> X, y = make_regression(
      ...     n_samples=200, n_features=2, noise=4.0, random_state=0)
      >>> reg = TheilSenRegressor(random_state=0).fit(X, y)
      >>> reg.score(X, y)
      0.9884...
      >>> reg.predict(X[:1,])
      array([-31.5871...])

  Methods

  `fit`(X, y) | Fit linear model.
  `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_params`(**params) | Set the parameters of this estimator.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.

  fit(X, y)

    Fit linear model.

    Parameters:
      X ndarray of shape (n_samples, n_features)

        Training data.

      y ndarray of shape (n_samples,)

        Target values.

    Returns:
      self returns an instance of self.

        Fitted `TheilSenRegressor` 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_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 = '$UNCHANGED$') → TheilSenRegressor

    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.TheilSenRegressor`

Robust linear estimator fitting

Robust linear estimator fitting

Theil-Sen Regression

Theil-Sen Regression