def compute_constants(self, y): """ Precomputes constants of the log density of the proposal distribution, which is Gaussian as p(x|y) ~ N(mu, R) where mu = y -a a = 0 R = gamma^2 I + M M^T M = 2 [\nabla_x k(x,z_i]|_x=y Returns (mu,L_R), where L_R is lower Cholesky factor of R """ assert(len(shape(y))==1) # M = 2 [\nabla_x k(x,z_i]|_x=y if self.Z is None: R = self.gamma ** 2 * eye(len(y)) else: M = 2 * self.kernel.gradient(y, self.Z) # R = gamma^2 I + \nu^2 * M H M^T H = Kernel.centring_matrix(len(self.Z)) R = self.gamma ** 2 * eye(len(y)) + self.nu2 * M.T.dot(H.dot(M)) L_R = cholesky(R) return y.copy(), L_R
def __init__(self, distribution, kernel, Z, nu2=0.1, gamma=0.1, num_eigen=10): Kameleon.__init__(self, distribution, kernel, Z, nu2, gamma) self.num_eigen = num_eigen if Z is None: self.Kc = None self.eigvalues = None self.eigvectors = None else: K = self.kernel.kernel(Z) H = Kernel.centring_matrix(len(self.Z)) self.Kc = H.dot(K.dot(H)) u, s, _ = svd(self.Kc) self.eigvalues = s[0 : self.num_eigen] self.eigvectors = u[:, 0 : self.num_eigen]
def construct_proposal(self, y): """ proposal is a mixture of normals, centred at y and with covariance gamma^2 I + nu^2 MHaa'HM', where a are the eigenvectors of centred kernel matrix Kc=HKH """ assert len(shape(y)) == 1 m = MixtureDistribution(self.distribution.dimension, self.num_eigen) m.mixing_proportion = Discrete((self.eigvalues + 1) / (sum(self.eigvalues) + self.num_eigen)) # print "current mixing proportion: ", m.mixing_proportion.omega M = 2 * self.kernel.gradient(y, self.Z) H = Kernel.centring_matrix(len(self.Z)) for ii in range(self.num_eigen): Sigma = self.gamma ** 2 * eye(len(y)) + self.nu2 * (M.T).dot( H.dot(outer(self.eigvectors[:, ii], self.eigvectors[:, ii]).dot(H.dot(M))) ) m.components[ii] = Gaussian(y, Sigma) return m
def construct_proposal(self, y): """ proposal is a mixture of normals, centred at y and with covariance gamma^2 I + nu^2 MHaa'HM', where a are the eigenvectors of centred kernel matrix Kc=HKH """ assert (len(shape(y)) == 1) m = MixtureDistribution(self.distribution.dimension, self.num_eigen) m.mixing_proportion = Discrete( (self.eigvalues + 1) / (sum(self.eigvalues) + self.num_eigen)) # print "current mixing proportion: ", m.mixing_proportion.omega M = 2 * self.kernel.gradient(y, self.Z) H = Kernel.centring_matrix(len(self.Z)) for ii in range(self.num_eigen): Sigma = self.gamma ** 2 * eye(len(y)) + \ self.nu2 * (M.T).dot(H.dot(outer(self.eigvectors[:, ii], self.eigvectors[:, ii]).dot(H.dot(M)))) m.components[ii] = Gaussian(y, Sigma) return m
def __init__(self, distribution, kernel, Z, nu2=0.1, gamma=0.1, num_eigen=10): Kameleon.__init__(self, distribution, kernel, Z, nu2, gamma) self.num_eigen = num_eigen if Z is None: self.Kc = None self.eigvalues = None self.eigvectors = None else: K = self.kernel.kernel(Z) H = Kernel.centring_matrix(len(self.Z)) self.Kc = H.dot(K.dot(H)) u, s, _ = svd(self.Kc) self.eigvalues = s[0:self.num_eigen] self.eigvectors = u[:, 0:self.num_eigen]