_nd=dZddlZddlmZmZddlmZddlZddl m Z ddl m Z ddl mZddlmZd d lmZd d lmZd d lmZd dlmZd dlmZmZd dlmZejejj Z!dZ"ddZ#dZ$dZ%GddeeZ&dS)z< A Theil-Sen Estimator for Multiple Linear Regression Model N)IntegralReal) combinations)linalg)binom)get_lapack_funcs)effective_n_jobs) LinearModel)RegressorMixin)check_random_state)Interval)delayedParallel)ConvergenceWarningcp||z }tjtj|dzd}|tk}t ||jdk}||}||ddtjf}tjtj||z d}|tkr>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 r axisrNg?) npsqrtsum_EPSILONintshapenewaxisrnormmaxmin)Xx_olddiff diff_normmask is_x_old_in_X quotient_norm new_directions ?lib/python3.11/site-packages/sklearn/linear_model/_theil_sen.py_modified_weiszfeld_stepr*s>6 u9DtQwQ///00I  D QWQZ/00M :D$2: .IKti'7a @ @ @AAMxqqqqzI5A>>> MB B B     C}}4455 E c==0 1 1E 9 :,MbP?c|jddkr*dtj|dfS|dz}tj|d}t |D]4}t ||}tj||z dz|krn1|}5tj d |t||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)keepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)max_iter) rrmedianravelmeanranger*rwarningswarnformatr)r!r0tolspatial_median_oldn_iterspatial_medians r)_spatial_medianr<QsD wqzQ")AGGII55555AIC+++//   1!5GHH 6%61< = = C C E!/    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. r g?) n_samples n_subsampless r)_breakdown_pointrAsG" A $ %\)AA)E F      r+ct|}|jd|z}|jd}tj|jd|f}tj||f}tjt ||}td||f\} t|D]D\} } || ddf|dd|df<|| |d|<| ||dd||| <E|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)gelssN) rrremptyoneszerosrr enumerate) r!yindices fit_intercept n_featuresr@weightsX_subpopulationy_subpopulationlstsqindexsubsets r)_lstsqrRs6 &&Mm+J=#Lh a(*566Gg|Z899OhL* = =??O _o,NOOHU"7++QQ v-.vqqqy\=>>)*)*6  &@@CKZKP Nr+c eZdZUdZdgdgeedddgdegeedddgeedddgd gdegd gd Zee d <d d dddddddd dZ dZ dZ dS)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...]) booleanr Nleft)closedrr random_stateverbose rJcopy_Xmax_subpopulationr@r0r8rXn_jobsrY_parameter_constraintsTg@r,r-Fc ||_||_||_||_||_||_||_||_| |_dSNrZ) selfrJr[r\r@r0r8rXr]rYs r)__init__zTheilSenRegressor.__init__RsK+ !2(  (  r+c |j}|jr|dz}n|}|||kr#td||||kr6||kr/|jrdnd}td|||n:||kr#td||nt ||}t dt jt||}tt |j |}||fS)Nr z=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@rJ ValueErrorr7r rrrintrrr\)rar?rKr@n_dimplus_1all_combinationsn_subpopulations r)_check_subparamsz"TheilSenRegressor._check_subparamsisE(   NEEE  #i'' --3VL)-L-LJ&&<''%)%7?TTRF$!6&%>>( 9,,$((.|Y(G(G-ui00Lq"'% <*H*H"I"IJJc$"8:JKKLL_,,r+c tj d\j\ } |\ _t _j rtd jtd tj z}td |td jtjt jkr+t#t%t'  }n" fdt'jD}t)j}tj|| t/|j  fd t'|D}tj|}t3|jj \_}jr|d _|d d _nd_|_S)aUFit linear model. Parameters ---------- X : ndarray of shape (n_samples, n_features) Training data. y : ndarray of shape (n_samples,) Target values. Returns ------- self : returns an instance of self. Fitted `TheilSenRegressor` estimator. T) y_numericzBreakdown point: {0}zNumber of samples: {0}zTolerable outliers: {0}zNumber of subpopulations: {0}c@g|]}dS)F)sizereplace)choice).0_r?r@rXs r) z)TheilSenRegressor.fit..s>##IL%#PPr+)r]rYc3nK|]/}tt|jV0dSr`)rrRrJ)rrjobr! index_listrarHs r) z(TheilSenRegressor.fit..s\@ @  GFOOAq*S/43E F F@ @ @ @ @ @ r+)r0r8rr Nr) _validate_paramsrrX_validate_datarrkn_subpopulation_rA breakdown_rYprintr7rrrfrr\listrr4r r] array_splitrvstackr<r0r8n_iter_rJ intercept_coef_) rar!rHrK tol_outliersrIr]rLcoefsrwr?r@rXs ``` @@@@r)fitzTheilSenRegressor.fits )$*;<< ""1a4"881 ! :.2.C.C z/ / + d++9lCC < Q (//@@ A A A *11)<< = = =t:;;L +22<@@ A A A 1889NOO P P P 75L11 2 2d6L L L<i(8(8,GGHHGGt455G "$+..^GV44 ?(&$,???@ @ @ @ @ @ @ V}}@ @ @   )G$$- dm    e   #AhDOqrrDJJ!DODJ r+) __name__ __module__ __qualname____doc__rrrr^dict__annotations__rbrkrr>r+r)rTrTsrrj$+&htQVDDDEx(Xh4???@sD8889'("; $ $D     .#-#-#-J:::::r+rT)r,r-)'rr5numbersrr itertoolsrnumpyrscipyr scipy.specialrscipy.linalg.lapackrjoblibr _baser baser utilsrutils._param_validationrutils.parallelrr exceptionsrfinfodoubleepsrr*r<rArRrTr>r+r)rs""""""""""""""000000######!!!!!!&&&&&&..............++++++ 28BI   "000f5"5"5"5"p6)))Xxxxxx xxxxxr+