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]
