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_interceptboolean, optional, default True

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

copy_Xboolean, optional, default True

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

max_subpopulationint, optional, 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, optional, 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, optional, default 300

Maximum number of iterations for the calculation of spatial median.

tolfloat, optional, default 1.e-3

Tolerance when calculating spatial median.

random_stateint, RandomState instance or None, optional, default None

A random number generator instance to define the state of the random permutations generator. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

n_jobsint or None, optional (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.

verboseboolean, optional, default False

Verbose mode when fitting the model.

Attributes
coef_array, 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

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(self, X, y)

Fit linear model.

get_params(self[, deep])

Get parameters for this estimator.

predict(self, X)

Predict using the linear model

score(self, X, y[, sample_weight])

Returns the coefficient of determination R^2 of the prediction.

set_params(self, \*\*params)

Set the parameters of this estimator.
__init__(self, 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]

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y)[source]

Fit linear model.

Parameters
Xnumpy array of shape [n_samples, n_features]

Training data

ynumpy array of shape [n_samples]

Target values

Returns
selfreturns an instance of self.
get_params(self, deep=True)[source]

Get parameters for this estimator.

Parameters
deepboolean, optional

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

Returns
paramsmapping of string to any

Parameter names mapped to their values.

predict(self, 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(self, X, y, sample_weight=None)[source]

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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, shape = (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator.

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

True values for X.

sample_weightarray-like, shape = [n_samples], optional

Sample weights.

Returns
scorefloat

R^2 of self.predict(X) wrt. y.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns
self