-i@HSrSSKrSSKJr SSKJrJr SSKrSSK J r SSK J r SSK Jr SSKJr S S KJrJr S S KJr S S KJr S S KJrJrJr S SKJrJr S SKJ r SSK!J"r" \RF"\RH5RJr&Sr'SSjr(Sr)Sr*"SS\\"5r+g)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) LinearModelc.X- n[R"[R"US-SS95nU[:n[ UR5UR S:5nX$nX4SS2[R 4n[R"[R"X#- SS95nU[:a8[R"XSS24U- SS9[R"SU- SS9- nOSnSn[SSXV- - 5U-[SXV- 5U--$)uModified 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 R/var/www/html/venv/lib/python3.13/site-packages/sklearn/linear_model/_theil_sen.py_modified_weiszfeld_stepr.s6 9DtQwQ/0I  D QWWQZ/0M :D2:: .IKKt'7a @AMxqqzI5A> MB     C}445 E c=0 1E 9 :cURSS:Xa%S[R"UR5SS94$US-n[R"USS9n[ U5H3n[ X5n[R"X5- S-5U:a XE4$UnM5 [R"SRUS9[5 WW4$) uSpatial 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%r2tolspatial_median_oldn_iterspatial_medians r-_spatial_medianr>PsD wwqzQ"))AGGI555AIC+/1!H 66%61< = C   !!"0  "   vxv(   > !!r/c:SSSU- -X- S--U-S- U- - $)zApproximation 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_pointrCsE" A $ %)AA)E F      r/c[U5nURSU-nURSn[R"URSU45n[R"XT45n[R "[ XT55n[SXx45un [U5H-upX SS24USS2US24'XUSU&U "Xx5SSUXj'M/ U$)aQLeast 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_featuresrBweightsX_subpopulationy_subpopulationlstsqindexsubsets r-_lstsqrTs6 &Mm+J==#Lhh a(*56Ggg|89OhhL =?O _,NOHU"7+ -.qy\=>)*)* &@CKZP, Nr/c \rSrSr%SrS/S\"\"S155/\"\SSSS9/S\ /\"\ S SSS9/\"\S SSS9/S /S\ /S /S . r \ \ S'SSSSSSSSSS . Sjr Sr\"SS9S5rSrg)TheilSenRegressoraoTheil-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 rLcopy_Xmax_subpopulationrBr2r:r\n_jobsr]_parameter_constraintsTg@,MbP?Fc pXlX lX0lX@lXPlX`lXplXlXlgNr^) selfrLr_r`rBr2r:r\rar]s r-__init__TheilSenRegressor.__init__Us5+ !2( (  r/c URnUR(aUS-nOUnUbzX1:a[SRX155eX:a6XC:a0UR(aSOSn[SRXTU55eO+X1:wa[SRX155eO [ XA5n[ S[ R"[X555n[[ URU55nX74$)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.) rBrL ValueErrorr9r$r#rrintr rr`)rgrArMrBn_dimplus_1all_combinationsn_subpopulations r-_check_subparams"TheilSenRegressor._check_subparamsls((   NEE  #' --3VL-L&'%)%7%7TRF$!6&>( ,$((.|(G-u0Lq"''% *H"IJc$"8"8:JKL,,r/)prefer_skip_nested_validationc ^^^^ TRS:wa[R"S[5 [ TR 5n[ TTTSS9ummTRupETRXE5unTl [XF5Tl TR(a[SRTR55 [SRU55 [TRU-5n[SRU55 [SRTR55 [ R""[%XF55TR&::a[)[+[-U5U55nO3[-TR5V s/sHn UR/XFS S 9PM nn [1TR25n [ R4"X5m [7U TRS 9"UU UU4S j[-U 555n [ R8"U 5n [;U TR<TR>S 9uTl n TRB(aU STl"U SSTl#T$STl"U Tl#T$s sn f)zFit 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. rYz`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}F)sizereplace)rar]c3n># UH*n[[5"TTTUTR5v M, g7frf)rrTrL).0jobr% index_listrgrJs r- (TheilSenRegressor.fit..s5@ $ FOAq*S/43E3E F F$s25)r2r:rrNr)$r_r7r8 FutureWarningrr\rr rrn_subpopulation_rC breakdown_r]printr9rrrmr r`listrr6choicerra array_splitrvstackr>r2r:n_iter_rL intercept_coef_)rgr%rJr\rArMrB tol_outliersrK_rarNcoefsr|s``` @r-fitTheilSenRegressor.fits! ;;, & MM/  *$*;*;< T1a481 ! .2.C.C / + d++9C << (//@ A *11)< =t:;L +22<@ A 1889N9NO P 7751 2d6L6L L<i(8,GHGt4455A##I%#P5  "$++.^^G4 &$,,?@ V}@  ))G$- dmm  e   #AhDOqrDJ  "DODJ /sI>)rrr_rLrr2r`rrarrBr\r:r])__name__ __module__ __qualname____firstlineno____doc__rrrrrrbdict__annotations__rhrrr r__static_attributes__r@r/r-rVrVsvr$fZ%?@A&tQVDEx(h4?@sD89'("; $D   .#-J5A6Ar/rV)rcrd),rr7 itertoolsrnumbersrrnumpyrjoblibrscipyrscipy.linalg.lapackr scipy.specialr baser r exceptionsr utilsrutils._param_validationrrrutils.parallelrrutils.validationr_baserfinfodoubleepsrr.r>rCrTrVr@r/r-rs{""#0/+&BB., 88BII  " "0f5"p6)XD Dr/