`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)[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.

Parameters

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.
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=1.e-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.

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.

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_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict using the linear model.
`score`(X, y[, sample_weight])	Return the coefficient of determination \(R^2\) of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y)[source]¶

Fit linear model.

Parameters

Xndarray of shape (n_samples, n_features): Training data.
yndarray of shape (n_samples,): Target values.

Returns

selfreturns an instance of self.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters

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

Returns

paramsdict: Parameter names mapped to their values.

predict(X)[source]¶

Predict using the linear model.

Parameters

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

Returns

Carray, shape (n_samples,): Returns predicted values.

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

Return the coefficient of determination \(R^2\) of the prediction.

The coefficient \(R^2\) 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

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.

Returns

scorefloat: \(R^2\) of self.predict(X) wrt. 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)[source]¶

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

**paramsdict: Estimator parameters.

Returns

selfestimator instance: Estimator instance.

Examples using `sklearn.linear_model.TheilSenRegressor`¶

sklearn.linear_model.TheilSenRegressor¶

Examples using sklearn.linear_model.TheilSenRegressor¶

`sklearn.linear_model`.TheilSenRegressor¶

Examples using `sklearn.linear_model.TheilSenRegressor`¶