def _stddev(self):
if distribution_util.is_diagonal_scale(self.scale):
stddev = tf.abs(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate)
and self.scale.is_self_adjoint):
stddev = tf.sqrt(
tf.linalg.diag_part(self.scale.matmul(self.scale.to_dense())))
else:
stddev = tf.sqrt(
tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(),
adjoint_arg=True)))
shape = tensorshape_util.concatenate(self.batch_shape,
self.event_shape)
has_static_shape = tensorshape_util.is_fully_defined(shape)
if not has_static_shape:
shape = tf.concat([
self.batch_shape_tensor(),
self.event_shape_tensor(),
], 0)
if has_static_shape and shape == stddev.shape:
return stddev
# Add dummy tensor of zeros to broadcast. This is only necessary if shape
# != stddev.shape, but we could not determine if this is the case.
return stddev + tf.zeros(shape, self.dtype)
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
return 2. * tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
return tf.matrix_diag_part(2. * self.scale.matmul(self.scale.to_dense()))
else:
return 2. * tf.matrix_diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True))
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
return 2. * tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
return tf.linalg.diag_part(2. * self.scale.matmul(self.scale.to_dense()))
else:
return 2. * tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True))
def _covariance(self):
if distribution_util.is_diagonal_scale(self.scale):
mvn_cov = tf.linalg.diag(tf.square(self.scale.diag_part()))
else:
mvn_cov = self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
cov_shape = tf.concat(
[self._sample_shape(), self._event_shape_tensor()], -1)
mvn_cov = tf.broadcast_to(mvn_cov, cov_shape)
return self._std_var_helper(mvn_cov, "covariance", 2, lambda x: x)
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
answer = tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
answer = tf.linalg.diag_part(self.scale.matmul(self.scale.to_dense()))
else:
answer = tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True))
return self._broadcast_variance_like_with_loc(answer)
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 tf.matrix_diag(tf.square(self.scale.diag_part()))
else:
return self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
def _stddev(self):
if distribution_util.is_diagonal_scale(self.scale):
return np.sqrt(2) * tf.abs(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
return np.sqrt(2) * tf.sqrt(
tf.matrix_diag_part(self.scale.matmul(self.scale.to_dense())))
else:
return np.sqrt(2) * tf.sqrt(
tf.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 tf.matrix_diag(tf.square(self.scale.diag_part()))
else:
return self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
mvn_var = tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
mvn_var = tf.linalg.diag_part(self.scale.matmul(self.scale.to_dense()))
else:
mvn_var = tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True))
mvn_var = tf.broadcast_to(mvn_var, self._sample_shape())
return self._std_var_helper(mvn_var, "variance", 1, lambda x: x)
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. * tf.matrix_diag(tf.square(self.scale.diag_part()))
else:
return 2. * 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. * tf.linalg.diag(tf.square(self.scale.diag_part()))
else:
return 2. * self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
return tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
return self.scale.matmul(self.scale.adjoint()).diag_part()
elif isinstance(self.scale, tf.linalg.LinearOperatorKronecker):
factors_sq_operators = [
factor.matmul(factor.adjoint()) for factor in self.scale.operators
]
return tf.linalg.LinearOperatorKronecker(factors_sq_operators).diag_part()
else:
return self.scale.matmul(self.scale.adjoint()).diag_part()
def _stddev(self):
if distribution_util.is_diagonal_scale(self.scale):
mvn_std = tf.abs(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
mvn_std = tf.sqrt(
tf.linalg.diag_part(self.scale.matmul(self.scale.to_dense())))
else:
mvn_std = tf.sqrt(
tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)))
mvn_std = tf.broadcast_to(mvn_std, self._sample_shape())
return self._std_var_helper(mvn_std, "standard deviation", 1, tf.sqrt)
def _covariance(self):
if distribution_util.is_diagonal_scale(self.scale):
cov = tf.linalg.diag(tf.square(self.scale.diag_part()))
else:
cov = self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
if self.loc is not None:
loc_shape = ps.shape(self.loc)
loc_plus_extra_event_shape = ps.concat([
loc_shape,
loc_shape[-1:],
], axis=0)
cov = tf.broadcast_to(
cov, ps.broadcast_shape(ps.shape(cov), loc_plus_extra_event_shape))
return cov
def _stddev(self):
if distribution_util.is_diagonal_scale(self.scale):
stddev = tf.abs(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate) and
self.scale.is_self_adjoint):
stddev = tf.sqrt(
tf.linalg.diag_part(self.scale.matmul(self.scale.to_dense())))
else:
stddev = tf.sqrt(
tf.linalg.diag_part(
self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)))
if self.loc is not None:
stddev = tf.broadcast_to(
stddev, ps.broadcast_shape(ps.shape(stddev), ps.shape(self.loc)))
return stddev
def _variance(self):
if distribution_util.is_diagonal_scale(self.scale):
variance = tf.square(self.scale.diag_part())
elif (isinstance(self.scale, tf.linalg.LinearOperatorLowRankUpdate)
and self.scale.is_self_adjoint):
variance = self.scale.matmul(self.scale.adjoint()).diag_part()
elif isinstance(self.scale, tf.linalg.LinearOperatorKronecker):
factors_sq_operators = [
factor.matmul(factor.adjoint())
for factor in self.scale.operators
]
variance = (tf.linalg.LinearOperatorKronecker(
factors_sq_operators).diag_part())
else:
variance = self.scale.matmul(self.scale.adjoint()).diag_part()
return tf.broadcast_to(
variance, ps.broadcast_shape(ps.shape(variance),
ps.shape(self.loc)))
def _covariance(self):
if distribution_util.is_diagonal_scale(self.scale):
return tf.matrix_diag(tf.square(self.scale.diag_part()))
else:
return self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)
def _covariance(self):
if distribution_util.is_diagonal_scale(self.scale):
return tf.matrix_diag(tf.square(self.scale.diag_part()))
else:
return self.scale.matmul(self.scale.to_dense(), adjoint_arg=True)