U 2‰d¢=ã@sòdZddlZddlmZmZddlmZddlZddl m Z ddl m Z ddl mZddlmZd d lmZd d lmZd d lmZd dlmZd dlmZmZd dlmZe ej¡j Z!dd„Z"ddd„Z#dd„Z$dd„Z%Gdd„deeƒZ&dS)z< A Theil-Sen Estimator for Multiple Linear Regression Model éN)ÚIntegralÚReal)Ú combinations)Úlinalg)Úbinom)Úget_lapack_funcs)Úeffective_n_jobsé)Ú LinearModelé)ÚRegressorMixin)Úcheck_random_state)ÚInterval)ÚdelayedÚParallel)ÚConvergenceWarningcCsÞ||}t tj|ddd¡}|tk}t| ¡|jdkƒ}||}||dd…tjf}t tj||dd¡}|tkr®tj||dd…f|ddtjd|dd}nd}d}t dd||ƒ|t d||ƒ|S)u Modified Weiszfeld step. This function defines one iteration step in order to approximate the spatial median (L1 median). It is a form of an iteratively re-weighted least squares method. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. x_old : ndarray of shape = (n_features,) Current start vector. Returns ------- x_new : ndarray of shape (n_features,) New iteration step. References ---------- - On Computation of Spatial Median for Robust Data Mining, 2005 T. Kärkkäinen and S. Äyrämö http://users.jyu.fi/~samiayr/pdf/ayramo_eurogen05.pdf r r ©ZaxisrNgð?ç) ÚnpÚsqrtÚsumÚ_EPSILONÚintÚshapeZnewaxisrZnormÚmaxÚmin)ÚXZx_oldZdiffZ diff_normÚmaskZ is_x_old_in_XZ quotient_normZ new_direction©rúC/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/linear_model/_theil_sen.pyÚ_modified_weiszfeld_steps$ ÿ ÿÿr é,çü©ñÒMbP?cCsŽ|jddkr$dtj| ¡ddfS|dC}tj|dd}t|ƒD].}t||ƒ}t ||d¡|krlq†qB|}qBt  dj |dt ¡||fS) u Spatial median (L1 median). The spatial median is member of a class of so-called M-estimators which are defined by an optimization problem. Given a number of p points in an n-dimensional space, the point x minimizing the sum of all distances to the p other points is called spatial median. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. max_iter : int, default=300 Maximum number of iterations. tol : float, default=1.e-3 Stop the algorithm if spatial_median has converged. Returns ------- spatial_median : ndarray of shape = (n_features,) Spatial median. n_iter : int Number of iterations needed. References ---------- - On Computation of Spatial Median for Robust Data Mining, 2005 T. Kärkkäinen and S. Äyrämö http://users.jyu.fi/~samiayr/pdf/ayramo_eurogen05.pdf r T)Zkeepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)Úmax_iter) rrZmedianZravelZmeanÚranger rÚwarningsÚwarnÚformatr)rr#ÚtolZspatial_median_oldZn_iterZspatial_medianrrrÚ_spatial_medianQs "  þür)cCs(ddd|||d|d|S)aApproximation of the breakdown point. Parameters ---------- n_samples : int Number of samples. n_subsamples : int Number of subsamples to consider. Returns ------- breakdown_point : float Approximation of breakdown point. r gà?r)Ú n_samplesÚ n_subsamplesrrrÚ_breakdown_point‰sÿþûÿÿr,c CsÂt|ƒ}|jd|}|jd}t |jd|f¡}t ||f¡}t t||ƒ¡}td||fƒ\} t|ƒD]R\} } || dd…f|dd…|d…f<|| |d|…<| ||ƒdd|…|| <qj|S)aLeast Squares Estimator for TheilSenRegressor class. This function calculates the least squares method on a subset of rows of X and y defined by the indices array. Optionally, an intercept column is added if intercept is set to true. Parameters ---------- X : array-like of shape (n_samples, n_features) Design matrix, where `n_samples` is the number of samples and `n_features` is the number of features. y : ndarray of shape (n_samples,) Target vector, where `n_samples` is the number of samples. indices : ndarray of shape (n_subpopulation, n_subsamples) Indices of all subsamples with respect to the chosen subpopulation. fit_intercept : bool Fit intercept or not. Returns ------- weights : ndarray of shape (n_subpopulation, n_features + intercept) Solution matrix of n_subpopulation solved least square problems. r r)ZgelssN) rrrÚemptyZonesÚzerosrrÚ enumerate) rÚyÚindicesÚ fit_interceptÚ n_featuresr+ÚweightsZX_subpopulationZy_subpopulationZlstsqÚindexZsubsetrrrÚ_lstsq¤s  r6c @sšeZdZUdZdgdgeeddddgdegeeddddgeeddddgd gdegd gd œ Zee d <d d dddddddd œ dd„Z dd„Z dd„Z dS)ÚTheilSenRegressoraRTheil-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 :ref:`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 :term:`Glossary `. n_jobs : int, default=None Number of CPUs to use during the cross validation. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`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 :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 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...]) Úbooleanr NÚleft)ÚclosedrrÚ random_stateÚverbose© r2Úcopy_XÚmax_subpopulationr+r#r(r;Ún_jobsr<Ú_parameter_constraintsTgˆÃ@r!r"Fc Cs:||_||_||_||_||_||_||_||_| |_dS©Nr=) Úselfr2r>r?r+r#r(r;r@r<rrrÚ__init__Rs zTheilSenRegressor.__init__cCs¾|j}|jr|d}n|}|dk r†||kr:td ||¡ƒ‚||krl||kr„|jrTdnd}td |||¡ƒ‚q||krtd ||¡ƒ‚n t||ƒ}tdt t||ƒ¡ƒ}t t|j |ƒƒ}||fS)Nr z=Invalid parameter since n_subsamples > n_samples ({0} > {1}).z+1ÚzAInvalid parameter since n_features{0} > n_subsamples ({1} > {2}).z\Invalid parameter since n_subsamples != n_samples ({0} != {1}) while n_samples < n_features.) r+r2Ú ValueErrorr'rrrÚrintrrr?)rCr*r3r+Zn_dimZplus_1Zall_combinationsZn_subpopulationrrrÚ_check_subparamsisB ÿÿþÿþÿ z"TheilSenRegressor._check_subparamsc sxˆ ¡tˆjƒ‰ˆjˆˆdd\‰‰ˆj\‰}ˆ ˆ|¡\‰ˆ_tˆˆƒˆ_ˆj ržt d  ˆj¡ƒt d  ˆ¡ƒt ˆjˆƒ}t d  |¡ƒt d  ˆj¡ƒt  tˆˆƒ¡ˆjkrÈtttˆƒˆƒƒ}n‡‡‡fdd„tˆjƒDƒ}tˆjƒ}t  ||¡‰t|ˆj d ‡‡‡‡fd d „t|ƒDƒƒ}t  |¡}t|ˆjˆjd \ˆ_}ˆjrh|d ˆ_|dd…ˆ_n dˆ_|ˆ_ˆS)aUFit 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. T)Z y_numericzBreakdown point: {0}zNumber of samples: {0}zTolerable outliers: {0}zNumber of subpopulations: {0}csg|]}ˆjˆˆdd‘qS)F)ÚsizeÚreplace)Úchoice)Ú.0Ú_)r*r+r;rrÚ ±sÿz)TheilSenRegressor.fit..)r@r<c3s&|]}ttƒˆˆˆ|ˆjƒVqdSrB)rr6r2)rLZjob)rÚ index_listrCr0rrÚ ¸sÿz(TheilSenRegressor.fit..)r#r(rr Nr) Z_validate_paramsr r;Z_validate_datarrHZn_subpopulation_r,Z breakdown_r<Úprintr'rrrGrr?Úlistrr$rr@Z array_splitrZvstackr)r#r(Zn_iter_r2Z intercept_Zcoef_) rCrr0r3Z tol_outliersr1r@r4Zcoefsr)rrOr*r+r;rCr0rÚfitŽsJ  ÿ  þ  þ ÿ  zTheilSenRegressor.fit) Ú__name__Ú __module__Ú __qualname__Ú__doc__rrrrAÚdictÚ__annotations__rDrHrSrrrrr7Ðs. uöõ %r7)r!r")'rWr%ZnumbersrrÚ itertoolsrZnumpyrZscipyrZ scipy.specialrZscipy.linalg.lapackrZjoblibrÚ_baser Úbaser Úutilsr Zutils._param_validationrZutils.parallelrrÚ exceptionsrZfinfoÚdoubleZepsrr r)r,r6r7rrrrÚs(           3 8,