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)[source]

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.

fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations.

copy_Xbool, default=True

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

max_subpopulationint, 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_subsamplesint, 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_iterint, default=300

Maximum number of iterations for the calculation of spatial median.

tolfloat, default=1e-3

Tolerance when calculating spatial median.

random_stateint, 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_jobsint, 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.

verbosebool, default=False

Verbose mode when fitting the model.

coef_ndarray of shape (n_features,)

Coefficients of the regression model (median of distribution).


Estimated intercept of regression model.


Approximated breakdown point.


Number of iterations needed for the spatial median.


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


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


Linear regression model that is robust to outliers.


RANSAC (RANdom SAmple Consensus) algorithm.


Fitted by minimizing a regularized empirical loss with SGD.



>>> 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)
>>> reg.predict(X[:1,])


fit(X, y)

Fit linear model.


Get parameters for this estimator.


Predict using the linear model.

score(X, y[, sample_weight])

Return the coefficient of determination of the prediction.


Set the parameters of this estimator.

fit(X, y)[source]

Fit linear model.

Xndarray of shape (n_samples, n_features)

Training data.

yndarray of shape (n_samples,)

Target values.

selfreturns an instance of self.

Fitted TheilSenRegressor estimator.


Get parameters for this estimator.

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.


Parameter names mapped to their values.


Predict using the linear model.

Xarray-like or sparse matrix, shape (n_samples, n_features)


Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None)[source]

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.

Xarray-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.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.


\(R^2\) of self.predict(X) w.r.t. y.


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 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.


Estimator parameters.

selfestimator instance

Estimator instance.

Examples using sklearn.linear_model.TheilSenRegressor

Robust linear estimator fitting

Robust linear estimator fitting

Robust linear estimator fitting
Theil-Sen Regression

Theil-Sen Regression

Theil-Sen Regression