{Kg=2dZddlZddlmZddlmZmZddlZddl m Z ddl m Z ddl mZddlmZd d lmZmZd d lmZd d lmZd d lmZd dlmZmZddlmZej>ej@jBZ"dZ#ddZ$dZ%dZ&GddeeZ'y)z< A Theil-Sen Estimator for Multiple Linear Regression Model N) combinations)IntegralReal)effective_n_jobs)linalg)get_lapack_funcs)binom)RegressorMixin _fit_context)ConvergenceWarning)check_random_state)Interval)Paralleldelayed) LinearModelcF||z }tjtj|dzd}|tk\}t |j|j dk}||}||ddtj f}tjtj||z d}|tkDr=tj||ddf|z dtjd|z dz }nd}d}tdd||z z |ztd||z |zzS)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 raxisrNg?) npsqrtsum_EPSILONintshapenewaxisrnormmaxmin)Xx_olddiff diff_normmask is_x_old_in_X quotient_norm new_directions c/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/sklearn/linear_model/_theil_sen.py_modified_weiszfeld_stepr+s6 u9DtQwQ/0I  D QWWQZ/0M :D$2:: .IKKti'7a @AMxqqzI5A> MB     C}}445 E c==0 1E 9 :c|jddk(r'dtj|jdfS|dz}tj|d}t |D]3}t ||}tj||z dz|kr||fS|}5tjdj|tfS) 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 rT)keepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)max_iter) rrmedianravelmeanranger+rwarningswarnformatr )r"r/tolspatial_median_oldn_iterspatial_medians r*_spatial_medianr;QsD wwqzQ"))AGGI555AIC+/1!5GH 66%61< = C  > !!"0  "   vxv(   > !!r,c<ddd|z z||z dzz|zdz |z z 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. rg?) n_samples n_subsampless r*_breakdown_pointr@sG" A $ %\)AA)E F      r,ct|}|jd|z}|jd}tj|jd|f}tj||f}tj t ||}td||f\} t|D]1\} } || ddf|dd|df<|| |d|| ||dd||| <3|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. rr)gelssN) rrremptyoneszerosr r enumerate) r"yindices fit_intercept n_featuresr?weightsX_subpopulationy_subpopulationlstsqindexsubsets r*_lstsqrQs6 &Mm+J==#Lhh a(*56Ggg|Z89OhhL* =?O _o,NOHU"7+ v-.vqy\=>)*)*6 &@CKZP, Nr,c eZdZUdZdgdgeedddgdegeedddgeedddgd gdegd gd Zee d <d d dddddddd dZ dZ e d dZ y)TheilSenRegressoraRTheil-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...]) booleanrNleft)closedrr random_stateverbose rIcopy_Xmax_subpopulationr?r/r7rWn_jobsrX_parameter_constraintsTg@,MbP?Fc ||_||_||_||_||_||_||_||_| |_yNrY) selfrIrZr[r?r/r7rWr\rXs r*__init__zTheilSenRegressor.__init__RsG+ !2(  (  r,c |j}|jr|dz}n|}|v||kDrtdj||||k\r1||kDrX|jrdnd}tdj|||||k7r'tdj||t ||}t dt jt||}tt |j|}||fS)Nrz=Invalid parameter since n_subsamples > n_samples ({0} > {1}).z+1zAInvalid 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?rI ValueErrorr6r!r rrintr rr[)rbr>rJr?n_dimplus_1all_combinationsn_subpopulations r*_check_subparamsz"TheilSenRegressor._check_subparamsis((   NEE  #i' --3VL)-LJ&<'%)%7%7TRF$!6&%>  9,$((.|Y(G ui0Lq"''% <*H"IJc$"8"8:JKL_,,r,)prefer_skip_nested_validationc tj}jd\j\}}j ||\}_t ||_jrtdjjtdj|tj|z}tdj|tdjj tjt||jkrt!t#t%||}n4t%j D cgc]} |j'||d}} t)j*} tj,||  t/| j  fd t%| D} tj0| } t3| j4j6 \_} j:r| d _| d d_Sd_| _Scc} w)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) y_numericzBreakdown point: {0}zNumber of samples: {0}zTolerable outliers: {0}zNumber of subpopulations: {0}F)sizereplace)r\rXc3hK|])}tt|j+ywra)rrQrI).0jobr" index_listrbrGs r* z(TheilSenRegressor.fit..s5@ $ GFOAq*S/43E3E F$s/2)r/r7rrNr) rrW_validate_datarrln_subpopulation_r@ breakdown_rXprintr6rrrgr r[listrr3choicerr\ array_splitrvstackr;r/r7n_iter_rI intercept_coef_)rbr"rGrWr>rJr? tol_outliersrH_r\rKcoefsrus``` @r*fitzTheilSenRegressor.fits *$*;*;< ""1a4"81 ! :.2.C.C z/ + d++9lC << (//@ A *11)< =t:;L +22<@ A 1889N9NO P 775L1 2d6L6L L<i(8,GHGt4455A##IL%#P5  "$++.^^GV4 ?(&$,,?@ V}@  ))G$- dmm  e   #AhDOqrDJ  "DODJ /s-I)__name__ __module__ __qualname____doc__rrrr]dict__annotations__rcrlr rr=r,r*rSrSsrj$+&tQVDEx(h4?@sD89'("; $D   .#-J5969r,rS)r^r_)(rr4 itertoolsrnumbersrrnumpyrjoblibrscipyrscipy.linalg.lapackr scipy.specialr baser r exceptionsr utilsrutils._param_validationrutils.parallelrr_baserfinfodoubleepsrr+r;r@rQrSr=r,r*rsw""#0/+&.. 288BII  " "0f5"p6)Xx xr,