def gaussian_mixture_logpdf(x, w, mu, Sigma):
# Shape(x) = (N, D)
# Shape(w) = (K,)
# Shape(mu) = (K, D)
# Shape(Sigma) = (K, D, D)
# Shape(result) = (N,)
# Dimensionality
D = np.shape(x)[-1]
# Cholesky decomposition of the covariance matrix
U = utils.m_chol(Sigma)
# Reshape x:
# Shape(x) = (N, 1, D)
x = np.expand_dims(x, axis=-2)
# (x-mu) and (x-mu)'*inv(Sigma)*(x-mu):
# Shape(v) = (N, K, D)
# Shape(z) = (N, K)
v = x - mu
z = np.einsum('...i,...i', v, utils.m_chol_solve(U, v))
# Log-determinant of Sigma:
# Shape(ldet) = (K,)
ldet = utils.m_chol_logdet(U)
# Compute log pdf for each cluster:
# Shape(lpdf) = (N, K)
lpdf = utils.gaussian_logpdf(z, 0, 0, ldet, D)
def compute_fixed_u_and_f(Lambda):
""" Compute u(x) and f(x) for given x. """
k = np.shape(Lambda)[-1]
ldet = utils.m_chol_logdet(utils.m_chol(Lambda))
u = [Lambda, ldet]
f = -(k + 1) / 2 * ldet
return (u, f)
def gaussian_mixture_logpdf(x, w, mu, Sigma):
# Shape(x) = (N, D)
# Shape(w) = (K,)
# Shape(mu) = (K, D)
# Shape(Sigma) = (K, D, D)
# Shape(result) = (N,)
# Dimensionality
D = np.shape(x)[-1]
# Cholesky decomposition of the covariance matrix
U = utils.m_chol(Sigma)
# Reshape x:
# Shape(x) = (N, 1, D)
x = np.expand_dims(x, axis=-2)
# (x-mu) and (x-mu)'*inv(Sigma)*(x-mu):
# Shape(v) = (N, K, D)
# Shape(z) = (N, K)
v = x - mu
z = np.einsum('...i,...i', v, utils.m_chol_solve(U, v))
# Log-determinant of Sigma:
# Shape(ldet) = (K,)
ldet = utils.m_chol_logdet(U)
# Compute log pdf for each cluster:
# Shape(lpdf) = (N, K)
lpdf = utils.gaussian_logpdf(z, 0, 0, ldet, D)
def compute_fixed_u_and_f(Lambda):
""" Compute u(x) and f(x) for given x. """
k = np.shape(Lambda)[-1]
ldet = utils.m_chol_logdet(utils.m_chol(Lambda))
u = [Lambda,
ldet]
f = -(k+1)/2 * ldet
return (u, f)
def _compute_moments_and_cgf(phi, mask=True):
U = utils.m_chol(-phi[0])
k = np.shape(phi[0])[-1]
#k = self.dims[0][0]
logdet_phi0 = utils.m_chol_logdet(U)
u0 = phi[1][..., np.newaxis, np.newaxis] * utils.m_chol_inv(U)
u1 = -logdet_phi0 + utils.m_digamma(phi[1], k)
u = [u0, u1]
g = phi[1] * logdet_phi0 - special.multigammaln(phi[1], k)
return (u, g)
def _compute_moments_and_cgf(phi, mask=True):
U = utils.m_chol(-phi[0])
k = np.shape(phi[0])[-1]
#k = self.dims[0][0]
logdet_phi0 = utils.m_chol_logdet(U)
u0 = phi[1][...,np.newaxis,np.newaxis] * utils.m_chol_inv(U)
u1 = -logdet_phi0 + utils.m_digamma(phi[1], k)
u = [u0, u1]
g = phi[1] * logdet_phi0 - special.multigammaln(phi[1], k)
return (u, g)
def compute_fixed_moments(Lambda):
""" Compute moments for fixed x. """
ldet = utils.m_chol_logdet(utils.m_chol(Lambda))
u = [Lambda, ldet]
return u
def compute_fixed_moments(Lambda):
""" Compute moments for fixed x. """
ldet = utils.m_chol_logdet(utils.m_chol(Lambda))
u = [Lambda,
ldet]
return u