o tBh<@sdZddlZddlZddlmZddlZddlmZddl m Z ddl m Z ddl mZmZdd lmZd d lmZd d lmZd d lmZd dlmZd dlmZeejjZddZ dddZ!ddZ"ddZ#GdddeeZ$dS)z< A Theil-Sen Estimator for Multiple Linear Regression Model N) combinations)linalg)binom)get_lapack_funcs)Paralleleffective_n_jobs) LinearModel)RegressorMixin)check_random_state) check_scalar)delayed)ConvergenceWarningcCs||}ttj|ddd}|tk}t||jdk}||}||ddtjf}ttj||dd}|tkrWtj||ddf|ddtjd|dd}nd}d}t dd|||t d|||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 raxisrNg?) npsqrtsum_EPSILONintshapenewaxisrnormmaxmin)Xx_olddiff diff_normmask is_x_old_in_X quotient_norm new_directionr%v/var/www/html/riverr-enterprise-integrations-main/venv/lib/python3.10/site-packages/sklearn/linear_model/_theil_sen.py_modified_weiszfeld_steps"  r',MbP?cCs|jddkrdtj|ddfS|dC}tj|dd}t|D]}t||}t||d|kr8||fS|}q!t 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 rT)keepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)max_iter) rrmedianravelmeanranger'rwarningswarnformatr)rr+tolspatial_median_oldn_iterspatial_medianr%r%r&_spatial_medianQs""   r7cCs(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. rg?r%) n_samples n_subsamplesr%r%r&_breakdown_pointsr:c Cst|}|jd|}|jd}t|jd|f}t||f}tt||}td||f\} t|D])\} } || ddf|dd|df<|| |d|<| ||dd||| <q5|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) rrremptyoneszerosrr enumerate) ryindices fit_intercept n_featuresr9weightsX_subpopulationy_subpopulationlstsqindexsubsetr%r%r&_lstsqs  rJc @s>eZdZdZdddddddddd d d Zd d Zd dZdS)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...]) Tg@Nr(r)F rBcopy_Xmax_subpopulationr9r+r3 random_staten_jobsverbosec Cs:||_||_||_||_||_||_||_||_| |_dSNrL) selfrBrMrNr9r+r3rOrPrQr%r%r&__init__Es  zTheilSenRegressor.__init__cCs|j}|jr |d}n|}|durC||krtd||||kr6||kr5|jr*dnd}td|||n||krBtd||nt||}t|jdtjtj fdd|_ t dt t||}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.rN) target_typemin_val)r9rB ValueErrorr2rr rNnumbersRealIntegral_max_subpopulationrrrintrr)rSr8rCr9n_dimplus_1all_combinationsn_subpopulationr%r%r&_check_subparams\sD    z"TheilSenRegressor._check_subparamsc sptjjdd\j\}|\_t_jrKt d jt d t j}t d |t d jt tjkr`ttt}nfddtjD}tj}t ||t|jd fd d t|D}t |}t|jjd \_}jr|d _|dd_Sd_|_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}csg|] }jddqS)F)sizereplace)choice).0_)r8r9rOr%r& sz)TheilSenRegressor.fit..)rPrQc3s(|]}tt|jVqdSrR)rrJrB)rgjob)r index_listrSr@r%r& s  z(TheilSenRegressor.fit..)r+r3rrNr)r rO_validate_datarrbn_subpopulation_r: breakdown_rQprintr2rrr]rr\listrr/rrP array_splitrvstackr7r+r3n_iter_rB intercept_coef_) rSrr@rC tol_outliersrArPrDcoefsr%)rrkr8r9rOrSr@r&fitsD         zTheilSenRegressor.fit)__name__ __module__ __qualname____doc__rTrbryr%r%r%r&rKsw  -rK)r(r))%r}r0rY itertoolsrnumpyrscipyr scipy.specialrscipy.linalg.lapackrjoblibrr_baser baser utilsr utils.validationr utils.fixesr exceptionsrfinfodoubleepsrr'r7r:rJrKr%r%r%r&s*            38,