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]¶ TheilSen 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, TheilSen is identical to least squares.
 max_iterint, default=300
Maximum number of iterations for the calculation of spatial median.
 tolfloat, default=1.e3
Tolerance when calculating spatial median.
 random_stateint or RandomState instance, 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 ajoblib.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
TheilSen 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
 paramsmapping of string to any
Parameter names mapped to their values.

predict
(X)[source]¶ Predict using the linear model.
 Parameters
 Xarraylike 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  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
 Xarraylike 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, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
R^2 of self.predict(X) wrt. y.
Notes
The R2 score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

set_params
(**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. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.