ó ‡ˆ\c@sŸdZddlZddlmZddlZddlmZmZm Z ddl m Z ddl m Z mZddlmZmZmZddlmZmZmZdd lmZmZmZdd lmZdd lmZdd l m!Z!m"Z"dd l#m$Z$ej%dddddgƒdd…ej&fZ'ej%dddddgƒdd…ej&fZ(defd„ƒYZ)deefd„ƒYZ*dS(s"Gaussian processes classification.iÿÿÿÿN(t itemgetter(tcholeskyt cho_solvetsolve(t fmin_l_bfgs_b(terftexpit(t BaseEstimatortClassifierMixintclone(tRBFtCompoundKerneltConstantKernel(t check_X_ytcheck_is_fittedt check_array(tcheck_random_state(t LabelEncoder(tOneVsRestClassifiertOneVsOneClassifier(tConvergenceWarningg= ×£p=Ú?gš™™™™™Ù?g®Gáz®×?g)\Âõ(Ü?gö(\ÂõØ?gÃ; !IûœÀgÄQfAÌy«@g>[(d©k@gîKìñ`@gv¨…úiŸÀt'_BinaryGaussianProcessClassifierLaplacecBskeZdZd dddeed d„Zd„Zd„Zd„Z d ed„Z ed „Z d „Z RS( sïBinary Gaussian process classification based on Laplace approximation. The implementation is based on Algorithm 3.1, 3.2, and 5.1 of ``Gaussian Processes for Machine Learning'' (GPML) by Rasmussen and Williams. Internally, the Laplace approximation is used for approximating the non-Gaussian posterior by a Gaussian. Currently, the implementation is restricted to using the logistic link function. .. versionadded:: 0.18 Parameters ---------- kernel : kernel object The kernel specifying the covariance function of the GP. If None is passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that the kernel's hyperparameters are optimized during fitting. optimizer : string or callable, optional (default: "fmin_l_bfgs_b") Can either be one of the internally supported optimizers for optimizing the kernel's parameters, specified by a string, or an externally defined optimizer passed as a callable. If a callable is passed, it must have the signature:: def optimizer(obj_func, initial_theta, bounds): # * 'obj_func' is the objective function to be maximized, which # takes the hyperparameters theta as parameter and an # optional flag eval_gradient, which determines if the # gradient is returned additionally to the function value # * 'initial_theta': the initial value for theta, which can be # used by local optimizers # * 'bounds': the bounds on the values of theta .... # Returned are the best found hyperparameters theta and # the corresponding value of the target function. return theta_opt, func_min Per default, the 'fmin_l_bfgs_b' algorithm from scipy.optimize is used. If None is passed, the kernel's parameters are kept fixed. Available internal optimizers are:: 'fmin_l_bfgs_b' n_restarts_optimizer: int, optional (default: 0) The number of restarts of the optimizer for finding the kernel's parameters which maximize the log-marginal likelihood. The first run of the optimizer is performed from the kernel's initial parameters, the remaining ones (if any) from thetas sampled log-uniform randomly from the space of allowed theta-values. If greater than 0, all bounds must be finite. Note that n_restarts_optimizer=0 implies that one run is performed. max_iter_predict: int, optional (default: 100) The maximum number of iterations in Newton's method for approximating the posterior during predict. Smaller values will reduce computation time at the cost of worse results. warm_start : bool, optional (default: False) If warm-starts are enabled, the solution of the last Newton iteration on the Laplace approximation of the posterior mode is used as initialization for the next call of _posterior_mode(). This can speed up convergence when _posterior_mode is called several times on similar problems as in hyperparameter optimization. See :term:`the Glossary `. copy_X_train : bool, optional (default: True) If True, a persistent copy of the training data is stored in the object. Otherwise, just a reference to the training data is stored, which might cause predictions to change if the data is modified externally. random_state : int, RandomState instance or None, optional (default: None) The generator used to initialize the centers. 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`. Attributes ---------- X_train_ : array-like, shape = (n_samples, n_features) Feature values in training data (also required for prediction) y_train_ : array-like, shape = (n_samples,) Target values in training data (also required for prediction) classes_ : array-like, shape = (n_classes,) Unique class labels. kernel_ : kernel object The kernel used for prediction. The structure of the kernel is the same as the one passed as parameter but with optimized hyperparameters L_ : array-like, shape = (n_samples, n_samples) Lower-triangular Cholesky decomposition of the kernel in X_train_ pi_ : array-like, shape = (n_samples,) The probabilities of the positive class for the training points X_train_ W_sr_ : array-like, shape = (n_samples,) Square root of W, the Hessian of log-likelihood of the latent function values for the observed labels. Since W is diagonal, only the diagonal of sqrt(W) is stored. log_marginal_likelihood_value_ : float The log-marginal-likelihood of ``self.kernel_.theta`` RiidcCsC||_||_||_||_||_||_||_dS(N(tkernelt optimizertn_restarts_optimizertmax_iter_predictt warm_startt copy_X_traint random_state(tselfRRRRRRR((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyt__init__”s      c sÒˆjd kr7tdddƒtdddƒˆ_ntˆjƒˆ_tˆjƒˆ_ˆj rst j |ƒn|ˆ_ t ƒ}|j|ƒˆ_|jˆ_ˆjjdkr×tdˆjjˆjfƒ‚n9ˆjjdkrtdjˆjjˆjjƒƒ‚nˆjd k rqˆjjd krqt‡fd †}ˆj|ˆjjˆjjƒg}ˆjd kr#t jˆjjƒjƒs td ƒ‚nˆjj}xttˆjƒD]`}t j ˆjj!|d d …d f|d d …dfƒƒ}|j"ˆj|||ƒƒq¼Wnt#t$t%dƒ|ƒƒ} |t j&| ƒd ˆj_t j'| ƒ ˆ_(nˆj)ˆjjƒˆ_(ˆjˆj ƒ} ˆj*| d tƒ\} \ˆ_+ˆ_,ˆ_-} } ˆS(sPFit Gaussian process classification model Parameters ---------- X : array-like, shape = (n_samples, n_features) Training data y : array-like, shape = (n_samples,) Target values, must be binary Returns ------- self : returns an instance of self. gð?tconstant_value_boundstfixedtlength_scale_boundsis=%s supports only binary classification. y contains classes %sis){0:s} requires 2 classes; got {1:d} classics?|r-ˆj|dtƒ\}}| | fSˆj|ƒ SdS(Nt eval_gradient(tlog_marginal_likelihoodtTrue(tthetaR"tlmltgrad(R(s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pytobj_funcÉs  sYMultiple optimizer restarts (n_restarts_optimizer>0) requires that all bounds are finite.Ntreturn_temporaries(.RtNonetCR tkernel_R RRtrngRtnptcopytX_train_Rt fit_transformty_train_tclasses_tsizet ValueErrort __class__t__name__tformatRtn_dimsR$t_constrained_optimizationR%tboundsRtisfinitetalltrangetexptuniformtappendtlisttmapRtargmintmintlog_marginal_likelihood_value_R#t_posterior_modetpi_tW_sr_tL_( RtXtyt label_encoderR(toptimaR;t iterationt theta_initialt lml_valuestKt_((Rs;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pytfitŸsN!    !    " 3cCstt|dddddgƒ|j|j|ƒ}|jj|j|jƒ}tj|dk|j d|j dƒS(s.Perform classification on an array of test vectors X. Parameters ---------- X : array-like, shape = (n_samples, n_features) Returns ------- C : array, shape = (n_samples,) Predicted target values for X, values are from ``classes_`` R0R2RHRIRJii( RR,R0tTtdotR2RHR.twhereR3(RRKtK_startf_star((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pytpredictös c CsIt|dddddgƒ|j|j|ƒ}|jj|j|jƒ}t|j|j dd…t j f|ƒ}|jj |ƒt j d||ƒ}dd |}t|}t jt j|ƒt|t j||td ƒƒd t j|d t jƒ}t|jd d ƒd tjƒ} t jd| | fƒjS( sÀReturn probability estimates for the test vector X. Parameters ---------- X : array-like, shape = (n_samples, n_features) Returns ------- C : array-like, shape = (n_samples, n_classes) Returns the probability of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute ``classes_``. R0R2RHRIRJNsij,ij->jiitaxisigà?(RR,R0RURVR2RHRRJRIR.tnewaxistdiagteinsumtLAMBDAStsqrttpiRtCOEFStsumtvstack( RRKRXRYtvt var_f_startalphatgammat integralstpi_star((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyt predict_proba s,%  U$cCs"|dkr(|r!tdƒ‚n|jS|jj|ƒ}|r^||jdtƒ\}}n||jƒ}|j|dtƒ\}\}}} } } |s¡|Stj |j dƒ} |dd…tj ft | tftj |ƒƒ} t| |dd…tj f|ƒ}dtj |ƒtjd||ƒ|d|dd |}xÅt| j dƒD]°}|dd…dd…|f}d | jj|ƒj| ƒd | jjƒj|jƒƒ}|j|j|ƒ} | |j| j| ƒƒ}||jj|ƒ| | jiigà?(R*R5RFR,tclone_with_thetaR0R$RGR.temptytshapeR\RR]RR^R>RURVtravelR2(RR%R"RRRt K_gradienttZRatW_srtLtbtatd_ZtRR+ts_2tjts_1ts_3((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR#3s.  *5&>?cCsã|jr<t|dƒr<|jj|jjkr<|j}ntj|jdtjƒ}tj }xOt |j ƒD]>}t |ƒ}|d|}tj |ƒ}|dd…tj f|} tj|jdƒ| |} t| dtƒ} |||j|} | |t| tf| j| ƒƒ} |j| ƒ}d| jj|ƒtjtj|jdd |ƒƒjƒtjtj| ƒƒjƒ}||d kr©Pn|}qqW||_|rÛ|||| | | ffS|SdS( s Mode-finding for binary Laplace GPC and fixed kernel. This approximates the posterior of the latent function values for given inputs and target observations with a Gaussian approximation and uses Newton's iteration to find the mode of this approximation. tf_cachedtdtypeiNitlowergà¿ig»½×Ùß|Û=(RthasattrR|RnR2R.t zeros_liketfloat64tinfR>RRR`R\teyeRR$RRVRUtlog1pR?RctlogR](RRRR)tfR#RSRatWRrtW_sr_KtBRsRtRuR&((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyRGvs.    &^  cCs¤|jdkrWt||d|ƒ\}}}|ddkrštjd|tƒqšnCt|jƒr‡|j||d|ƒ\}}ntd|jƒ‚||fS(NRR;twarnflagis7fmin_l_bfgs_b terminated abnormally with the state: %ssUnknown optimizer %s.(RRtwarningstwarnRtcallableR5(RR(t initial_thetaR;t theta_opttfunc_mintconvergence_dict((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR:«s  !N( R7t __module__t__doc__R*tFalseR$RRTRZRkR#RGR:(((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR$so W  'C 5tGaussianProcessClassifierc BskeZdZd dddeed dd d„ Zd„Zd„Zd„Z e d „ƒZ d ed „Z RS( sÈGaussian process classification (GPC) based on Laplace approximation. The implementation is based on Algorithm 3.1, 3.2, and 5.1 of Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams. Internally, the Laplace approximation is used for approximating the non-Gaussian posterior by a Gaussian. Currently, the implementation is restricted to using the logistic link function. For multi-class classification, several binary one-versus rest classifiers are fitted. Note that this class thus does not implement a true multi-class Laplace approximation. Parameters ---------- kernel : kernel object The kernel specifying the covariance function of the GP. If None is passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that the kernel's hyperparameters are optimized during fitting. optimizer : string or callable, optional (default: "fmin_l_bfgs_b") Can either be one of the internally supported optimizers for optimizing the kernel's parameters, specified by a string, or an externally defined optimizer passed as a callable. If a callable is passed, it must have the signature:: def optimizer(obj_func, initial_theta, bounds): # * 'obj_func' is the objective function to be maximized, which # takes the hyperparameters theta as parameter and an # optional flag eval_gradient, which determines if the # gradient is returned additionally to the function value # * 'initial_theta': the initial value for theta, which can be # used by local optimizers # * 'bounds': the bounds on the values of theta .... # Returned are the best found hyperparameters theta and # the corresponding value of the target function. return theta_opt, func_min Per default, the 'fmin_l_bfgs_b' algorithm from scipy.optimize is used. If None is passed, the kernel's parameters are kept fixed. Available internal optimizers are:: 'fmin_l_bfgs_b' n_restarts_optimizer : int, optional (default: 0) The number of restarts of the optimizer for finding the kernel's parameters which maximize the log-marginal likelihood. The first run of the optimizer is performed from the kernel's initial parameters, the remaining ones (if any) from thetas sampled log-uniform randomly from the space of allowed theta-values. If greater than 0, all bounds must be finite. Note that n_restarts_optimizer=0 implies that one run is performed. max_iter_predict : int, optional (default: 100) The maximum number of iterations in Newton's method for approximating the posterior during predict. Smaller values will reduce computation time at the cost of worse results. warm_start : bool, optional (default: False) If warm-starts are enabled, the solution of the last Newton iteration on the Laplace approximation of the posterior mode is used as initialization for the next call of _posterior_mode(). This can speed up convergence when _posterior_mode is called several times on similar problems as in hyperparameter optimization. See :term:`the Glossary `. copy_X_train : bool, optional (default: True) If True, a persistent copy of the training data is stored in the object. Otherwise, just a reference to the training data is stored, which might cause predictions to change if the data is modified externally. random_state : int, RandomState instance or None, optional (default: None) The generator used to initialize the centers. 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`. multi_class : string, default : "one_vs_rest" Specifies how multi-class classification problems are handled. Supported are "one_vs_rest" and "one_vs_one". In "one_vs_rest", one binary Gaussian process classifier is fitted for each class, which is trained to separate this class from the rest. In "one_vs_one", one binary Gaussian process classifier is fitted for each pair of classes, which is trained to separate these two classes. The predictions of these binary predictors are combined into multi-class predictions. Note that "one_vs_one" does not support predicting probability estimates. n_jobs : int or None, optional (default=None) The number of jobs to use for the computation. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Attributes ---------- kernel_ : kernel object The kernel used for prediction. In case of binary classification, the structure of the kernel is the same as the one passed as parameter but with optimized hyperparameters. In case of multi-class classification, a CompoundKernel is returned which consists of the different kernels used in the one-versus-rest classifiers. log_marginal_likelihood_value_ : float The log-marginal-likelihood of ``self.kernel_.theta`` classes_ : array-like, shape = (n_classes,) Unique class labels. n_classes_ : int The number of classes in the training data Examples -------- >>> from sklearn.datasets import load_iris >>> from sklearn.gaussian_process import GaussianProcessClassifier >>> from sklearn.gaussian_process.kernels import RBF >>> X, y = load_iris(return_X_y=True) >>> kernel = 1.0 * RBF(1.0) >>> gpc = GaussianProcessClassifier(kernel=kernel, ... random_state=0).fit(X, y) >>> gpc.score(X, y) # doctest: +ELLIPSIS 0.9866... >>> gpc.predict_proba(X[:2,:]) array([[0.83548752, 0.03228706, 0.13222543], [0.79064206, 0.06525643, 0.14410151]]) .. versionadded:: 0.18 Riidt one_vs_restc CsU||_||_||_||_||_||_||_||_| |_dS(N( RRRRRRRt multi_classtn_jobs( RRRRRRRRR—R˜((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyRBs        cCst||dtƒ\}}t|j|j|j|j|j|j|j ƒ|_ t j |ƒ|_ |j j|_|jdkr¤td|j|j dfƒ‚n|jdkr#|jdkràt|j d|jƒ|_ q#|jdkr t|j d|jƒ|_ q#td |jƒ‚n|j j||ƒ|jdkryt jg|j jD]}|jƒ^qXƒ|_n|j jƒ|_|S( sPFit Gaussian process classification model Parameters ---------- X : array-like, shape = (n_samples, n_features) Training data y : array-like, shape = (n_samples,) Target values, must be binary Returns ------- self : returns an instance of self. t multi_outputisfGaussianProcessClassifier requires 2 or more distinct classes; got %d class (only class %s is present)iiR–R˜t one_vs_onesUnknown multi-class mode %s(R R”RRRRRRRRtbase_estimator_R.tuniqueR3R4t n_classes_R5R—RR˜RRTtmeant estimators_R#RF(RRKRLt estimator((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyRTPs4  +cCs/t|ddgƒt|ƒ}|jj|ƒS(s.Perform classification on an array of test vectors X. Parameters ---------- X : array-like, shape = (n_samples, n_features) Returns ------- C : array, shape = (n_samples,) Predicted target values for X, values are from ``classes_`` R3R(RRR›RZ(RRK((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyRZ†s  cCs\t|ddgƒ|jdkr@|jdkr@tdƒ‚nt|ƒ}|jj|ƒS(s¾Return probability estimates for the test vector X. Parameters ---------- X : array-like, shape = (n_samples, n_features) Returns ------- C : array-like, shape = (n_samples, n_classes) Returns the probability of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute `classes_`. R3RiRšslone_vs_one multi-class mode does not support predicting probability estimates. Use one_vs_rest mode instead.(RRR—R5RR›Rk(RRK((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyRk–s  cCsC|jdkr|jjStg|jjD]}|j^q)ƒSdS(Ni(RR›R,R RŸ(RR ((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR,¬s  c Cs€t|ddgƒ|d kr;|r4tdƒ‚n|jStj|ƒ}|jdkrl|jj||ƒS|rt dƒ‚n|jj }|dj j }|j d|kråtjgt|ƒD]\}}|j|ƒ^qÃS|j d||jj dkrNtjgt|ƒD].\}}|j|||||d!ƒ^qƒStd|||jj d|j dfƒ‚d S( sÎReturns log-marginal likelihood of theta for training data. In the case of multi-class classification, the mean log-marginal likelihood of the one-versus-rest classifiers are returned. Parameters ---------- theta : array-like, shape = (n_kernel_params,) or none Kernel hyperparameters for which the log-marginal likelihood is evaluated. In the case of multi-class classification, theta may be the hyperparameters of the compound kernel or of an individual kernel. In the latter case, all individual kernel get assigned the same theta values. If None, the precomputed log_marginal_likelihood of ``self.kernel_.theta`` is returned. eval_gradient : bool, default: False If True, the gradient of the log-marginal likelihood with respect to the kernel hyperparameters at position theta is returned additionally. Note that gradient computation is not supported for non-binary classification. If True, theta must not be None. Returns ------- log_likelihood : float Log-marginal likelihood of theta for training data. log_likelihood_gradient : array, shape = (n_kernel_params,), optional Gradient of the log-marginal likelihood with respect to the kernel hyperparameters at position theta. Only returned when eval_gradient is True. R3Rs.Gradient can only be evaluated for theta!=NoneisHGradient of log-marginal-likelihood not implemented for multi-class GPC.iisEShape of theta must be either %d or %d. Obtained theta with shape %d.N(RR*R5RFR.tasarrayRR›R#tNotImplementedErrorRŸR,R9RnRžt enumerateR3(RR%R"t estimatorsR9tiR ((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR#µs4       ,!?N( R7R’R“R*R”R$RRTRZRktpropertyR,R#(((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyR•¼s…  6   (+R“R‹toperatorRtnumpyR.t scipy.linalgRRRtscipy.optimizeRt scipy.specialRRt sklearn.baseRRR t sklearn.gaussian_process.kernelsR R R R+tsklearn.utils.validationR RRt sklearn.utilsRtsklearn.preprocessingRtsklearn.multiclassRRtsklearn.exceptionsRtarrayR\R_RbRR•(((s;lib/python2.7/site-packages/sklearn/gaussian_process/gpc.pyts&   1"ÿ™