def expected_stats(self):
mean, nu, a, B = self.to_standard()
D = mean.shape[-1]
maha, B_tril = mahalanobis(B, mean)
logdet_B = 2. * triangular_logdet(B_tril)
expec_lambda2 = -.5 * a[..., None, None] * cholseky_inverse(B_tril)
expec_lambda1 = -2. * matvec(expec_lambda2, mean)
expec_log_norm = .5 * (a * maha + D / nu + mvdigamma(a, D) - logdet_B)
return expec_lambda1, expec_lambda2, expec_log_norm
def _log_normalizer(self):
return torch.lgamma(.5 * self.df) - torch.lgamma(.5 * (self.df + self.loc.shape[-1])) \
+ .5 * torch.log(math.pi * self.df) + triangular_logdet(self.scale_tril)
def log_normalizer(self):
D = self.event_shape[-1]
return torch.mvlgamma(self.concentration, D) + self.concentration \
* (D * math.log(2.) + 2. * LA.triangular_logdet(self.scale_tril))
def expected_logdet(self):
D = self.event_shape[-1]
return mvdigamma(self.concentration, D) + D * math.log(2.) \
+ 2. * LA.triangular_logdet(self.scale_tril)
def entropy(self) -> torch.Tensor:
logdet = triangular_logdet(self.scale_tril)
return .5 * self.event_shape[0] * (1. + _LOG_2PI) + logdet
def _log_normalizer(self, nat_param1, nat_param2):
maha, prec_tril = mahalanobis(-2. * nat_param2, nat_param1)
logdet = triangular_logdet(prec_tril)
return .5 * maha - logdet + .5 * self.event_shape[0] * _LOG_2PI