U <|e=@sdZddlZddlmZmZddlmZddlZddl m Z ddl m Z ddl mZddlmZd d lmZd d lmZd d lmZd dlmZd dlmZmZd dlmZeejj Z!ddZ"dddZ#ddZ$ddZ%GdddeeZ&dS)z< A Theil-Sen Estimator for Multiple Linear Regression Model N)IntegralReal) combinations)linalg)binom)get_lapack_funcs)effective_n_jobs) LinearModel)RegressorMixin)check_random_state)Interval)delayedParallel)ConvergenceWarningcCs||}ttj|ddd}|tk}t||jdk}||}||ddtjf}ttj||dd}|tkrtj||ddf|ddtjd|dd}nd}d}t dd|||t d|||S)u Modified Weiszfeld step. This function defines one iteration step in order to approximate the spatial median (L1 median). It is a form of an iteratively re-weighted least squares method. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. x_old : ndarray of shape = (n_features,) Current start vector. Returns ------- x_new : ndarray of shape (n_features,) New iteration step. References ---------- - On Computation of Spatial Median for Robust Data Mining, 2005 T. Kärkkäinen and S. Äyrämö http://users.jyu.fi/~samiayr/pdf/ayramo_eurogen05.pdf r r axisrNg?) npsqrtsum_EPSILONintshapenewaxisrnormmaxmin)Xx_olddiffZ diff_normmaskZ is_x_old_in_XZ quotient_normZ new_directionr#\/var/www/website-v5/atlas_env/lib/python3.8/site-packages/sklearn/linear_model/_theil_sen.py_modified_weiszfeld_steps$  r%,MbP?cCs|jddkr$dtj|ddfS|dC}tj|dd}t|D].}t||}t||d|krlqqB|}qBt dj |dt ||fS) u Spatial median (L1 median). The spatial median is member of a class of so-called M-estimators which are defined by an optimization problem. Given a number of p points in an n-dimensional space, the point x minimizing the sum of all distances to the p other points is called spatial median. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. max_iter : int, default=300 Maximum number of iterations. tol : float, default=1.e-3 Stop the algorithm if spatial_median has converged. Returns ------- spatial_median : ndarray of shape = (n_features,) Spatial median. n_iter : int Number of iterations needed. References ---------- - On Computation of Spatial Median for Robust Data Mining, 2005 T. Kärkkäinen and S. Äyrämö http://users.jyu.fi/~samiayr/pdf/ayramo_eurogen05.pdf r T)keepdimsr rrzYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.)max_iter) rrmedianravelmeanranger%rwarningswarnformatr)rr)tolZspatial_median_oldn_iterZspatial_medianr#r#r$_spatial_medianQs "  r3cCs(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. r g?r#) n_samples n_subsamplesr#r#r$_breakdown_pointsr6c Cst|}|jd|}|jd}t|jd|f}t||f}tt||}td||f\} t|D]R\} } || ddf|dd|df<|| |d|<| ||dd||| <qj|S)aLeast Squares Estimator for TheilSenRegressor class. This function calculates the least squares method on a subset of rows of X and y defined by the indices array. Optionally, an intercept column is added if intercept is set to true. Parameters ---------- X : array-like of shape (n_samples, n_features) Design matrix, where `n_samples` is the number of samples and `n_features` is the number of features. y : ndarray of shape (n_samples,) Target vector, where `n_samples` is the number of samples. indices : ndarray of shape (n_subpopulation, n_subsamples) Indices of all subsamples with respect to the chosen subpopulation. fit_intercept : bool Fit intercept or not. Returns ------- weights : ndarray of shape (n_subpopulation, n_features + intercept) Solution matrix of n_subpopulation solved least square problems. r r)gelssN) rrremptyoneszerosrr enumerate) ryindices fit_intercept n_featuresr5weightsZX_subpopulationZy_subpopulationlstsqindexsubsetr#r#r$_lstsqs  rDc @seZdZUdZdgdgeeddddgdegeeddddgeeddddgd gdegd gd Zee d <d d dddddddd ddZ ddZ ddZ 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 r>copy_Xmax_subpopulationr5r)r1rIn_jobsrJ_parameter_constraintsTg@r&r'Fc Cs:||_||_||_||_||_||_||_||_| |_dSNrK) selfr>rLrMr5r)r1rIrNrJr#r#r$__init__Rs zTheilSenRegressor.__init__cCs|j}|jr|d}n|}|dk r||kr:td||||krl||kr|jrTdnd}td|||q||krtd||n t||}tdtt||}t t|j |}||fS)Nr z=Invalid parameter since n_subsamples > n_samples ({0} > {1}).z+1zAInvalid parameter since n_features{0} > n_subsamples ({1} > {2}).z\Invalid parameter since n_subsamples != n_samples ({0} != {1}) while n_samples < n_features.) r5r> ValueErrorr0rrrrintrrrM)rQr4r?r5n_dimZplus_1Zall_combinationsZn_subpopulationr#r#r$_check_subparamsisB  z"TheilSenRegressor._check_subparamsc sxtjjdd\j\}|\_t_j rt d jt d t j}t d |t d jt tjkrttt}nfddtjD}tj}t ||t|j d fd d t|D}t |}t|jjd \_}jrh|d _|dd_n d_|_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_)r4r5rIr#r$ sz)TheilSenRegressor.fit..)rNrJc3s&|]}tt|jVqdSrP)rrDr>)r\job)r index_listrQr<r#r$ sz(TheilSenRegressor.fit..)r)r1rr Nr) _validate_paramsr rI_validate_datarrWZn_subpopulation_r6Z breakdown_rJprintr0rrrUrrMlistrr-rrN array_splitrvstackr3r)r1n_iter_r> intercept_coef_) rQrr<r?Z tol_outliersr=rNr@coefsr#)rr`r4r5rIrQr<r$fitsJ         zTheilSenRegressor.fit) __name__ __module__ __qualname____doc__rrrrOdict__annotations__rRrWrlr#r#r#r$rEs. u %rE)r&r')'rpr.numbersrr itertoolsrnumpyrscipyr scipy.specialrZscipy.linalg.lapackrjoblibr_baser baser utilsr utils._param_validationrZutils.parallelrr exceptionsrfinfodoubleepsrr%r3r6rDrEr#r#r#r$s(           3 8,