0Ph@6dZddlZddlmZddlmZmZddlZddl m Z ddl m Z ddl mZddlmZd d lmZmZd d lmZd d lmZd d lmZmZmZd dlmZmZd dlm Z ddl!m"Z"ej#ej$j%Z&dZ'ddZ(dZ)dZ*Gddee"Z+dS)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)HiddenInterval StrOptions)Paralleldelayed) validate_data) LinearModelcp||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 raxisrNg?) npsqrtsum_EPSILONintshapenewaxisrnormmaxmin)Xx_olddiff diff_normmask is_x_old_in_X quotient_norm new_directions _/var/www/html/test/jupyter/venv/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 rT)keepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)max_iter) r rmedianravelmeanranger.rwarningswarnformatr )r%r4tolspatial_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. rg?) n_samples n_subsampless r-_breakdown_pointrEsG" 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. rr)gelssN) rr remptyoneszerosr#r enumerate) r%yindices fit_intercept n_featuresrDweightsX_subpopulationy_subpopulationlstsqindexsubsets r-_lstsqrVs6 &&Mm+J=#Lh a(*566Gg|Z899OhL* = =??O _o,NOOHU"7++QQ v-.vqqqy\=>>)*)*6  &@@CKZKP Nr/c eZdZUdZdgdeedhgeedddgdegeedddgeed ddgd gdegd gd Z e e d <dddddddddd dZ dZ eddZdS)TheilSenRegressoraTheil-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. .. deprecated:: 1.6 `copy_X` was deprecated in 1.6 and will be removed in 1.8. It has no effect as a copy is always made. 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...]) boolean deprecatedrNleft)closedrr random_stateverbose rNcopy_Xmax_subpopulationrDr4r<r]n_jobsr^_parameter_constraintsTg@r0r1Fc ||_||_||_||_||_||_||_||_| |_dSNr_) selfrNr`rarDr4r<r]rbr^s r-__init__zTheilSenRegressor.__init__VsK+ !2(  (  r/c |j}|jr|dz}n|}|||kr#td||||kr6||kr/|jrdnd}td|||n:||kr#td||nt ||}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.) rDrN ValueErrorr;r$r#rrintr rra)rfrCrOrDn_dimplus_1all_combinationsn_subpopulations r-_check_subparamsz"TheilSenRegressor._check_subparamsmsE(   NEEE  #i'' --3VL)-L-LJ&&<''%)%7?TTRF$!6&%>>( 9,,$((.|Y(G(G-ui00Lq"'% <*H*H"I"IJJc$"8:JKKLL_,,r/)prefer_skip_nested_validationc jdkrtjdtt j t d\j\ } |\ _ t _ j rtdj td tj z}td|tdj t!jt% jkr+t)t+t-  }n" fd t-j D}t/j}t!j|| t5|j  fd t-|D}t!j|}t9|jj \_}j r|d _!|dd_"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. rZz`copy_X` was deprecated in 1.6 and will be removed in 1.8 since it has no effect internally. Simply leave this parameter to its default value to avoid this warning.T) y_numericzBreakdown point: {0}zNumber of samples: {0}zTolerable outliers: {0}zNumber of subpopulations: {0}c@g|]}dS)F)sizereplace)choice).0_rCrDr]s r- z)TheilSenRegressor.fit..s>##IL%#PPr/)rbr^c3nK|]/}tt|jV0dSre)rrVrN)rxjobr% index_listrfrLs r- z(TheilSenRegressor.fit..s\@ @  GFOOAq*S/43E F F@ @ @ @ @ @ r/)r4r<rrNr)#r`r9r: FutureWarningrr]rr rpn_subpopulation_rE breakdown_r^printr;rrrkr ralistrr8rrb array_splitrvstackr@r4r<n_iter_rN intercept_coef_) rfr%rLrO tol_outliersrMrbrPcoefsr}rCrDr]s ``` @@@@r-fitzTheilSenRegressor.fits ;, & & M/    *$*;<< T1a48881 ! :.2.C.C z/ / + d++9lCC < Q (//@@ A A A *11)<< = = =t:;;L +22<@@ A A A 1889NOO P P P 75L11 2 2d6L L L<i(8(8,GGHHGGt455G "$+..^GV44 ?(&$,???@ @ @ @ @ @ @ V}}@ @ @   )G$$- dm    e   #AhDOqrrDJJ!DODJ r/)__name__ __module__ __qualname____doc__rrrrrrcdict__annotations__rgrpr rrBr/r-rXrXs@vvr$ffZZ%?%?@@A&htQVDDDEx(Xh4???@sD8889'("; $ $D     .#-#-#-J\555AA65AAAr/rX)r0r1),rr9 itertoolsrnumbersrrnumpyrjoblibrscipyrscipy.linalg.lapackr scipy.specialr baser r exceptionsr utilsrutils._param_validationrrrutils.parallelrrutils.validationr_baserfinfodoubleepsrr.r@rErVrXrBr/r-rs""""""""""""""######000000////////++++++&&&&&&BBBBBBBBBB........,,,,,, 28BI   "000f5"5"5"5"p6)))XDDDDD DDDDDr/