def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
return 2. * math_ops.square(self.scale.diag_part())
elif (isinstance(self.scale, linalg.LinearOperatorLowRankUpdate)
and self.scale.is_self_adjoint):
return array_ops.matrix_diag_part(
2. * self.scale.matmul(self.scale.to_dense()))
else:
return 2. * array_ops.matrix_diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True))
def _covariance(self):
# Let
# W = (w1,...,wk), with wj ~ iid Exponential(0, 1).
# Then this distribution is
# X = loc + LW,
# and then since Cov(wi, wj) = 1 if i=j, and 0 otherwise,
# Cov(X) = L Cov(W W^T) L^T = L L^T.
if distribution_util.is_diagonal_scale(self.scale):
return array_ops.matrix_diag(math_ops.square(self.scale.diag_part()))
else:
return self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
def _covariance(self):
# Let
# W = (w1,...,wk), with wj ~ iid Laplace(0, 1).
# Then this distribution is
# X = loc + LW,
# and since E[X] = loc,
# Cov(X) = E[LW W^T L^T] = L E[W W^T] L^T.
# Since E[wi wj] = 0 if i != j, and 2 if i == j, we have
# Cov(X) = 2 LL^T
if distribution_util.is_diagonal_scale(self.scale):
return 2. * array_ops.matrix_diag(
math_ops.square(self.scale.diag_part()))
else:
return 2. * self.scale.matmul(self.scale.to_dense(),
adjoint_arg=True)