def check(self, value):
# check for diagonal equal to 1
unit_variance = torch.all(
torch.abs(torch.diagonal(value, dim1=-2, dim2=-1) - 1) < 1e-6, dim=-1
)
# TODO: fix upstream - positive_definite has an extra dimension in front of output shape
return positive_definite.check(value) & unit_variance
def _log_prob(self, parameter):
if not positive_definite.check(parameter):
raise ValueError(
"parameter must be positive definite for Wishart prior")
return self.C + 0.5 * (
(self.nu - self.shape[0] - 1) * torch.log(torch.det(parameter)) -
torch.trace(self.K_inv.matmul(parameter)))
def _log_prob(self, parameter):
if not positive_definite.check(parameter):
raise ValueError(
"parameter must be positive definite for Inverse Wishart prior"
)
return self.C - 0.5 * (
(self.nu + 2 * self.shape[0]) * torch.log(torch.det(parameter)) +
torch.trace(torch.gesv(self.K, parameter)[0]))
def is_valid_correlation_matrix(Sigma, tol=1e-6):
""" This function returns true when all diagonal elements of Sigma are
strictly 1 (in a float sense) and the matrix is positive definite,
and false otherwise.
"""
pdef = positive_definite.check(Sigma)
return bool(torch.all(
torch.abs(Sigma.diag() - 1) < tol)) if pdef else False
def __init__(self, nu, K):
if not positive_definite.check(K):
raise ValueError("K must be positive definite")
n = K.shape[0]
if nu <= n:
raise ValueError("Must have nu > n - 1")
super(WishartPrior, self).__init__()
self.register_buffer("K_inv", torch.inverse(K))
self.register_buffer("nu", torch.Tensor([nu]))
# normalization constant
C = -(nu / 2 * torch.log(torch.det(K)) + nu * n / 2 * math.log(2) +
log_mv_gamma(n, nu / 2))
self.register_buffer("C", C)
self._log_transform = False
def __init__(self, nu, K):
n = K.shape[0]
if not positive_definite.check(K):
raise ValueError("K must be positive definite")
if nu <= 0:
raise ValueError("Must have nu > 0")
super(InverseWishartPrior, self).__init__()
self.register_buffer("K", K)
self.register_buffer("nu", torch.Tensor([nu]))
# normalization constant
c = (nu + n - 1) / 2
C = c * torch.log(torch.det(K)) - c * n * math.log(2) - log_mv_gamma(
n, c)
self.register_buffer("C", C)
self._log_transform = False
def is_in_support(self, parameter):
return bool(positive_definite.check(parameter))