def rotate(self, R, inv=None, logdet=None):
if inv is not None:
invR = inv
else:
invR = np.linalg.inv(R)
if logdet is not None:
logdetR = logdet
else:
logdetR = np.linalg.slogdet(R)[1]
# It would be more efficient and simpler, if you just rotated the
# moments and didn't touch phi. However, then you would need to call
# update() before lower_bound_contribution. This is more error-safe.
# Transform parameters
self.phi[0] = linalg.mvdot(invR.T, self.phi[0])
self.phi[1] = linalg.dot(invR.T, self.phi[1], invR)
self.phi[2] = linalg.dot(invR.T, self.phi[2], invR)
N = self.dims[0][0]
if False:
self._update_moments_and_cgf()
else:
# Transform moments and g
u0 = linalg.mvdot(R, self.u[0])
u1 = linalg.dot(R, self.u[1], R.T)
u2 = linalg.dot(R, self.u[2], R.T)
self.u = [u0, u1, u2]
self.g -= N*logdetR
def rotate(self, R, inv=None, logdet=None):
if inv is not None:
invR = inv
else:
invR = np.linalg.inv(R)
if logdet is not None:
logdetR = logdet
else:
logdetR = np.linalg.slogdet(R)[1]
# It would be more efficient and simpler, if you just rotated the
# moments and didn't touch phi. However, then you would need to call
# update() before lower_bound_contribution. This is more error-safe.
#print('rotate debug in gmc', self.phi[0])
#print(R, invR, np.shape(self.phi[0]))
# Transform parameters
self.phi[0] = mvdot(invR.T, self.phi[0])
self.phi[1] = dot(invR.T, self.phi[1], invR)
self.phi[2] = dot(invR.T, self.phi[2], invR)
N = self.dims[0][0]
if False:
#print(self.phi[0])
self._update_moments_and_cgf()
else:
# Transform moments and g
u0 = mvdot(R, self.u[0])
u1 = dot(R, self.u[1], R.T)
u2 = dot(R, self.u[2], R.T)
self.u = [u0, u1, u2]
self.g -= N * logdetR
def rotate(self, R, inv=None, logdet=None, Q=None):
raise NotImplementedError()
if inv is not None:
invR = inv
else:
invR = np.linalg.inv(R)
if logdet is not None:
logdetR = logdet
else:
logdetR = np.linalg.slogdet(R)[1]
# It would be more efficient and simpler, if you just rotated the
# moments and didn't touch phi. However, then you would need to call
# update() before lower_bound_contribution. This is more error-safe.
# Rotate plates, if plate rotation matrix is given. Assume that there's
# only one plate-axis
#logdet_old = np.sum(utils.linalg.logdet_cov(-2*self.phi[1]))
if Q is not None:
# Rotate moments using Q
self.u[0] = np.einsum('ik,kj->ij', Q, self.u[0])
sumQ = np.sum(Q, axis=0)
# Rotate natural parameters using Q
self.phi[1] = np.einsum('d,dij->dij', sumQ**(-2), self.phi[1])
self.phi[0] = np.einsum('dij,dj->di', -2*self.phi[1], self.u[0])
# Transform parameters using R
self.phi[0] = mvdot(invR.T, self.phi[0])
self.phi[1] = dot(invR.T, self.phi[1], invR)
if Q is not None:
self._update_moments_and_cgf()
else:
# Transform moments and g using R
self.u[0] = mvdot(R, self.u[0])
self.u[1] = dot(R, self.u[1], R.T)
self.g -= logdetR
def rotate(self, R, inv=None, logdet=None, Q=None):
if inv is not None:
invR = inv
else:
invR = np.linalg.inv(R)
if logdet is not None:
logdetR = logdet
else:
logdetR = np.linalg.slogdet(R)[1]
# It would be more efficient and simpler, if you just rotated the
# moments and didn't touch phi. However, then you would need to call
# update() before lower_bound_contribution. This is more error-safe.
# Rotate plates, if plate rotation matrix is given. Assume that there's
# only one plate-axis
#logdet_old = np.sum(utils.linalg.logdet_cov(-2*self.phi[1]))
if Q is not None:
# Rotate moments using Q
self.u[0] = np.einsum('ik,kj->ij', Q, self.u[0])
sumQ = np.sum(Q, axis=0)
# Rotate natural parameters using Q
self.phi[1] = np.einsum('d,dij->dij', sumQ**(-2), self.phi[1])
self.phi[0] = np.einsum('dij,dj->di', -2 * self.phi[1], self.u[0])
# Transform parameters using R
self.phi[0] = mvdot(invR.T, self.phi[0])
self.phi[1] = dot(invR.T, self.phi[1], invR)
if Q is not None:
self._update_moments_and_cgf()
else:
# Transform moments and g using R
self.u[0] = mvdot(R, self.u[0])
self.u[1] = dot(R, self.u[1], R.T)
self.g -= logdetR
def _compute_message_to_parent(self, index, m, *u_parents):
"""
Compute the message to a parent node.
.. math::
(\sum_i \mathbf{x}_i)^T \mathbf{M}_2 (\sum_j \mathbf{x}_j)
+ (\sum_i \mathbf{x}_i)^T \mathbf{m}_1
Moments of the parents are
.. math::
u_1^{(i)} = \langle \mathbf{x}_i \rangle
\\
u_2^{(i)} = \langle \mathbf{x}_i \mathbf{x}_i^T \rangle
Thus, the message for :math:`i`-th parent is
.. math::
\phi_{x_i}^{(1)} = \mathbf{m}_1 + 2 \mathbf{M}_2 \sum_{j\neq i} \mathbf{x}_j
\\
\phi_{x_i}^{(2)} = \mathbf{M}_2
"""
# Remove the moments of the parent that receives the message
u_parents = u_parents[:index] + u_parents[(index + 1):]
m0 = (m[0] +
linalg.mvdot(2 * m[1],
functools.reduce(np.add,
(u_parent[0]
for u_parent in u_parents)),
ndim=self.ndim))
m1 = m[1]
return [m0, m1]
def _compute_message_to_parent(self, index, m, *u_parents):
"""
Compute the message to a parent node.
.. math::
(\sum_i \mathbf{x}_i)^T \mathbf{M}_2 (\sum_j \mathbf{x}_j)
+ (\sum_i \mathbf{x}_i)^T \mathbf{m}_1
Moments of the parents are
.. math::
u_1^{(i)} = \langle \mathbf{x}_i \rangle
\\
u_2^{(i)} = \langle \mathbf{x}_i \mathbf{x}_i^T \rangle
Thus, the message for :math:`i`-th parent is
.. math::
\phi_{x_i}^{(1)} = \mathbf{m}_1 + 2 \mathbf{M}_2 \sum_{j\neq i} \mathbf{x}_j
\\
\phi_{x_i}^{(2)} = \mathbf{M}_2
"""
# Remove the moments of the parent that receives the message
u_parents = u_parents[:index] + u_parents[(index+1):]
m0 = (m[0] +
linalg.mvdot(
2*m[1],
functools.reduce(np.add,
(u_parent[0] for u_parent in u_parents)),
ndim=self.ndim))
m1 = m[1]
return [m0, m1]