physbo.gp.inf.exact のソースコード

# SPDX-License-Identifier: MPL-2.0
# Copyright (C) 2020- The University of Tokyo
#
# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at https://mozilla.org/MPL/2.0/.

import numpy as np
import scipy
from ... import misc
from copy import deepcopy


[ドキュメント] def eval_marlik(gp, X, t, params=None): """ Evaluating marginal likelihood. Parameters ---------- gp: physbo.gp.core.model X: numpy.ndarray N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate. t: numpy.ndarray N dimensional array. The negative energy of each search candidate (value of the objective function to be optimized). params: numpy.ndarray Parameters. Returns ------- marlik: float Marginal likelihood. """ ndata, ndims = X.shape lik_params, prior_params = gp.decomp_params(params) fmu = gp.prior.get_mean(ndata, params=prior_params) G = gp.prior.get_cov(X, params=prior_params) B = gp.lik.get_cov(ndata, params=lik_params) A = G + B + 1e-8 * np.identity(ndata) res = t - fmu U = scipy.linalg.cholesky(A, check_finite=False) alpha = scipy.linalg.solve_triangular( U.transpose(), res, lower=True, overwrite_b=False, check_finite=False ) marlik = ( 0.5 * ndata * np.log(2 * np.pi) + np.sum(np.log(np.diag(U))) + 0.5 * np.inner(alpha, alpha) ) return marlik
[ドキュメント] def get_grad_marlik(gp, X, t, params=None): """ Evaluating gradiant of marginal likelihood. Parameters ---------- gp: physbo.gp.core.model X: numpy.ndarray N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate. t: numpy.ndarray N dimensional array. The negative energy of each search candidate (value of the objective function to be optimized). params: numpy.ndarray Parameters. Returns ------- grad_marlik: numpy.ndarray Gradiant of marginal likelihood. """ ndata, ndims = X.shape lik_params, prior_params = gp.decomp_params(params) fmu = gp.prior.get_mean(ndata, prior_params) G = gp.prior.get_cov(X, params=prior_params) B = gp.lik.get_cov(ndata, lik_params) A = G + B + 1e-8 * np.identity(ndata) U = scipy.linalg.cholesky(A, check_finite=False) res = t - fmu alpha = misc.gauss_elim(U, res) invA = scipy.linalg.inv(A, check_finite=False) grad_marlik = np.zeros(gp.num_params) """ lik """ if gp.lik.num_params != 0: lik_grad = gp.lik.get_grad(ndata, lik_params) temp = lik_grad.dot(alpha) grad_marlik[0 : gp.lik.num_params] = -0.5 * temp.dot( alpha ) + 0.5 * misc.traceAB2(invA, lik_grad) ntemp = gp.lik.num_params """ prior """ if gp.prior.mean.num_params != 0: mean_grad = gp.prior.get_grad_mean(ndata, prior_params) grad_marlik[ntemp : ntemp + gp.prior.mean.num_params] = -np.inner( alpha, mean_grad ) ntemp += gp.prior.mean.num_params if gp.prior.cov.num_params != 0: cov_grad = gp.prior.get_grad_cov(X, prior_params) temp = cov_grad.dot(alpha) grad_marlik[ntemp:] = -0.5 * temp.dot(alpha) + 0.5 * misc.traceAB3( invA, cov_grad ) return grad_marlik
[ドキュメント] def prepare(gp, X, t, params=None): """ Parameters ---------- gp: physbo.gp.core.model X: numpy.ndarray N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate. t: numpy.ndarray N dimensional array. The negative energy of each search candidate (value of the objective function to be optimized). params: numpy.ndarray Parameters. Returns ------- stats: tupple """ ndata = X.shape[0] ndims = X.shape[1] if params is None: params = np.copy(gp.params) lik_params, prior_params = gp.decomp_params(params) G = gp.prior.get_cov(X, params=prior_params) fmu = gp.prior.get_mean(ndata, params=prior_params) B = gp.lik.get_cov(ndata, params=lik_params) A = G + B + 1e-8 * np.identity(ndata) U = scipy.linalg.cholesky(A, check_finite=False) residual = t - fmu alpha = misc.gauss_elim(U, residual) stats = (U, alpha) return stats
[ドキュメント] def get_post_fmean(gp, X, Z, params=None): """ Calculating the mean of posterior Parameters ---------- gp: physbo.gp.core.model X: numpy.ndarray N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate. Z: numpy.ndarray N x d dimensional matrix. Each row of Z denotes the d-dimensional feature vector of tests. params: numpy.ndarray Parameters. Returns ------- numpy.ndarray """ ndata = X.shape[0] ndims = X.shape[1] ntest = Z.shape[0] lik_params, prior_params = gp.decomp_params(params) alpha = gp.stats[1] fmu = gp.prior.get_mean(ntest) G = gp.prior.get_cov(X=Z, Z=X, params=prior_params) return G.dot(alpha) + fmu
[ドキュメント] def get_post_fcov(gp, X, Z, params=None, diag=True): """ Calculating the covariance of posterior Parameters ---------- gp: physbo.gp.core.model X: numpy.ndarray N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate. Z: numpy.ndarray N x d dimensional matrix. Each row of Z denotes the d-dimensional feature vector of tests. params: numpy.ndarray Parameters. diag: bool If X is the diagonalization matrix, true. Returns ------- numpy.ndarray """ lik_params, prior_params = gp.decomp_params(params) U = gp.stats[0] alpha = gp.stats[1] G = gp.prior.get_cov(X=X, Z=Z, params=prior_params) invUG = scipy.linalg.solve_triangular( U.transpose(), G, lower=True, overwrite_b=False, check_finite=False ) if diag: diagK = gp.prior.get_cov(X=Z, params=prior_params, diag=True) diag_invUG2 = misc.diagAB(invUG.transpose(), invUG) post_cov = diagK - diag_invUG2 else: K = gp.prior.get_cov(X=Z, params=prior_params) post_cov = K - np.dot(invUG.transpose(), invUG) return post_cov