ó ‡ˆ\c@`sRdZddlmZmZmZddlZddlmZddlZ ddl m Z ddl m Z ddlmZdd lmZd d lmZd d lmZd d lmZd dlmZmZmZd dlmZd dlmZe je j ƒj!Z"d„Z#ddd„Z$d„Z%d„Z&deefd„ƒYZ'dS(s< A Theil-Sen Estimator for Multiple Linear Regression Model i(tdivisiontprint_functiontabsolute_importN(t combinations(tlinalg(tbinom(tget_lapack_funcsi(t LinearModeli(tRegressorMixin(tcheck_random_state(t check_X_y(tParalleltdelayedteffective_n_jobs(txrange(tConvergenceWarningcC`s)||}tjtj|dddƒƒ}|tk}t|jƒ|jdkƒ}||}||dd…tjf}tjtj||ddƒƒ}|tkrïtj||dd…f|ddƒtjd|ddƒ}n d}d}t dd||ƒ|t d||ƒ|S(søModified 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, 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 : array, shape = [n_features] Current start vector. Returns ------- x_new : array, 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 itaxisiiNgð?g( tnptsqrttsumt_EPSILONtinttshapetnewaxisRtnormtmaxtmin(tXtx_oldtdifft diff_normtmaskt is_x_old_in_Xt quotient_normt new_direction((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyt_modified_weiszfeld_steps "  " &i,gü©ñÒMbP?cC`s¾|jddkr,dtj|jƒƒfS|dC}tj|ddƒ}xft|ƒD]<}t||ƒ}tj||dƒ|krŽPqX|}qXWtj dj d|ƒt ƒ||fS(sSpatial 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, 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, optional Maximum number of iterations. Default is 300. tol : float, optional Stop the algorithm if spatial_median has converged. Default is 1.e-3. Returns ------- spatial_median : array, 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 iiRisYMaximum number of iterations {max_iter} reached in spatial median for TheilSen regressor.tmax_iter( RRtmediantraveltmeantrangeR#RtwarningstwarntformatR(RR$ttoltspatial_median_oldtn_itertspatial_median((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyt_spatial_medianOs"   cC`s(ddd|||d|d|S(sApproximation 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. igà?((t n_samplest n_subsamples((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyt_breakdown_point…sc C`st|ƒ}|jd|}|jd}tj|jd|fƒ}tj||fƒ}tjt||ƒƒ}td||fƒ\} xot|ƒD]a\} } || dd…f|dd…|d…f<|| ||*| ||ƒd| || `. Parameters ---------- fit_intercept : boolean, optional, default True Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations. copy_X : boolean, optional, default True If True, X will be copied; else, it may be overwritten. max_subpopulation : int, optional, 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. n_subsamples : int, optional, 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, optional, default 300 Maximum number of iterations for the calculation of spatial median. tol : float, optional, default 1.e-3 Tolerance when calculating spatial median. random_state : int, RandomState instance or None, optional, default None A random number generator instance to define the state of the random permutations generator. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. n_jobs : int or None, optional (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 : boolean, optional, default False Verbose mode when fitting the model. Attributes ---------- coef_ : array, 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. 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) # doctest: +ELLIPSIS 0.9884... >>> reg.predict(X[:1,]) array([-31.5871...]) 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 gˆÃ@i,gü©ñÒMbP?c C`s[||_||_t|ƒ|_||_||_||_||_||_| |_ dS(N( R;tcopy_XRtmax_subpopulationR2R$R,t random_statetn_jobstverbose( tselfR;RERFR2R$R,RGRHRI((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyt__init__*s       cC`sL|j}|jr|d}n|}|dk rÐ||krXtdj||ƒƒ‚n||kr¦||krÍ|jrdnd}tdj|||ƒƒ‚qÍqß||krßtdj||ƒƒ‚qßnt||ƒ}|jdkr tdj|jƒƒ‚ntdtj t ||ƒƒƒ}t t|j|ƒƒ}||fS( Nis=Invalid parameter since n_subsamples > n_samples ({0} > {1}).s+1tsAInvalid parameter since n_features{0} > n_subsamples ({1} > {2}).s\Invalid parameter since n_subsamples != n_samples ({0} != {1}) while n_samples < n_features.is3Subpopulation must be strictly positive ({0} <= 0).( R2R;tNonet ValueErrorR+RRFRRtrintRR(RJR1R<R2tn_dimtplus_1tall_combinationstn_subpopulation((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyt_check_subparams7s2            !c `stˆjƒ}tˆˆdtƒ\‰‰ˆj\}}ˆj||ƒ\}ˆ_t||ƒˆ_ˆj r×t dj ˆjƒƒt dj |ƒƒt ˆj|ƒ}t dj |ƒƒt dj ˆjƒƒnt jt||ƒƒˆjkrttt|ƒ|ƒƒ}n7gtˆjƒD]!} |j|d|dtƒ^q&}tˆjƒ} t j|| ƒ‰td| d ˆj ƒ‡‡‡‡fd †t| ƒDƒƒ} t j| ƒ} t| d ˆjd ˆjƒ\ˆ_} ˆjr| d ˆ_ | dˆ_!ndˆ_ | ˆ_!ˆS(s(Fit linear model. Parameters ---------- X : numpy array of shape [n_samples, n_features] Training data y : numpy array of shape [n_samples] Target values Returns ------- self : returns an instance of self. t y_numericsBreakdown point: {0}sNumber of samples: {0}sTolerable outliers: {0}sNumber of subpopulations: {0}tsizetreplaceRHRIc3`s1|]'}ttƒˆˆˆ|ˆjƒVqdS(N(R RCR;(t.0tjob(Rt index_listRJR9(s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pys …sR$R,iig("R RGR tTrueRRTtn_subpopulation_R3t breakdown_RItprintR+RRRORRFtlistRR(tchoicetFalseR RHt array_splitR tvstackR0R$R,tn_iter_R;t intercept_tcoef_( RJRR9RGR1R<R2t tol_outliersR:t_RHR=tcoefs((RRZRJR9s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pytfit\sB   !4        N( t__name__t __module__t__doc__R[RMRaRKRTRj(((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyRDÆs b  %((Rmt __future__RRRR)t itertoolsRtnumpyRtscipyRt scipy.specialRtscipy.linalg.lapackRtbaseRRtutilsR R t utils._joblibR R R texternals.six.movesRR(t exceptionsRtfinfotdoubletepsRR#R0R3RCRD(((s=lib/python2.7/site-packages/sklearn/linear_model/theil_sen.pyts(   06  -