def _stats_ensure_array(stats):
ysq, yxT, xxT, n = stats
if yxT.ndim != 2:
raise Exception("yxT.shape must be (D_out, D_in)")
D_out, D_in = yxT.shape
# If ysq is D_out x D_out, just take the diagonal
if ysq.ndim == 1:
assert ysq.shape == (D_out, )
elif ysq.ndim == 2:
assert ysq.shape == (D_out, D_out)
ysq = np.diag(ysq)
else:
raise Exception("ysq.shape must be (D_out,) or (D_out, D_out)")
# Make sure xxT is D_out x D_in x D_in
if xxT.ndim == 2:
assert xxT.shape == (D_in, D_in)
xxT = np.tile(xxT[None, :, :], (D_out, 1, 1))
elif xxT.ndim == 3:
assert xxT.shape == (D_out, D_in, D_in)
else:
raise Exception(
"xxT.shape must be (D_in, D_in) or (D_out, D_in, D_in)")
# Make sure n is of shape (D_out,)
if np.isscalar(n):
n = n * np.ones(D_out)
elif n.ndim == 1:
assert n.shape == (D_out, )
else:
raise Exception("n must be a scalar or an array of shape (D_out,)")
return objarray([ysq, yxT, xxT, n])
def _stats_ensure_array(stats):
ysq, yxT, xxT, n = stats
if yxT.ndim != 2:
raise Exception("yxT.shape must be (D_out, D_in)")
D_out, D_in = yxT.shape
# If ysq is D_out x D_out, just take the diagonal
if ysq.ndim == 1:
assert ysq.shape == (D_out,)
elif ysq.ndim == 2:
assert ysq.shape == (D_out, D_out)
ysq = np.diag(ysq)
else:
raise Exception("ysq.shape must be (D_out,) or (D_out, D_out)")
# Make sure xxT is D_out x D_in x D_in
if xxT.ndim == 2:
assert xxT.shape == (D_in, D_in)
xxT = np.tile(xxT[None,:,:], (D_out, 1, 1))
elif xxT.ndim == 3:
assert xxT.shape == (D_out, D_in, D_in)
else:
raise Exception("xxT.shape must be (D_in, D_in) or (D_out, D_in, D_in)")
# Make sure n is of shape (D_out,)
if np.isscalar(n):
n = n * np.ones(D_out)
elif n.ndim == 1:
assert n.shape == (D_out,)
else:
raise Exception("n must be a scalar or an array of shape (D_out,)")
return objarray([ysq, yxT, xxT, n])
def _null_stats(self):
return objarray([
np.zeros(self.D_obs),
np.zeros((self.D_obs, self.D_latent)),
np.zeros((self.D_obs, self.D_latent, self.D_latent)),
np.zeros(self.D_obs)
])
def _set_expected_stats(self):
D_lat = self.D_latent
E_Xsq = np.sum(self.X**2 * self.mask, axis=0)
E_XZT = (self.X * self.mask).T.dot(self.E_Z)
E_ZZT_vec = self.E_ZZT.reshape((self.E_ZZT.shape[0], D_lat ** 2))
E_ZZT = np.array([np.dot(self.mask[:, d], E_ZZT_vec).reshape((D_lat, D_lat))
for d in range(self.D_obs)])
n = np.sum(self.mask, axis=0)
self.E_emission_stats = objarray([E_Xsq, E_XZT, E_ZZT, n])
def _set_expected_stats(self):
D_lat = self.D_latent
E_Xsq = np.sum(self.X**2 * self.mask, axis=0)
E_XZT = (self.X * self.mask).T.dot(self.E_Z)
E_ZZT_vec = self.E_ZZT.reshape((self.E_ZZT.shape[0], D_lat ** 2))
E_ZZT = np.array([np.dot(self.mask[:, d], E_ZZT_vec).reshape((D_lat, D_lat))
for d in range(self.D_obs)])
n = np.sum(self.mask, axis=0)
self.E_emission_stats = objarray([E_Xsq, E_XZT, E_ZZT, n])
def _set_expected_stats(self, smoothed_mus, smoothed_sigmas, E_xtp1_xtT):
if self.mask is None:
return super(LDSStatesMissingData, self).\
_set_expected_stats(smoothed_mus, smoothed_sigmas, E_xtp1_xtT)
# Get the emission stats
p, n, d, T, mask, inputs, data = \
self.D_emission, self.D_latent, self.D_input, self.T, \
self.mask, self.inputs, self.data
E_x_xT = smoothed_sigmas + self.smoothed_mus[:, :,
None] * self.smoothed_mus[:,
None, :]
E_x_uT = smoothed_mus[:, :, None] * self.inputs[:, None, :]
E_u_uT = self.inputs[:, :, None] * self.inputs[:, None, :]
E_xu_xuT = np.concatenate(
(np.concatenate((E_x_xT, E_x_uT), axis=2),
np.concatenate((np.transpose(E_x_uT,
(0, 2, 1)), E_u_uT), axis=2)),
axis=1)
E_xut_xutT = E_xu_xuT[:-1].sum(0)
E_xtp1_xtp1T = E_x_xT[1:].sum(0)
E_xt_xtT = E_x_xT[:-1].sum(0)
E_xtp1_xtT = E_xtp1_xtT.sum(0)
E_xtp1_utT = (smoothed_mus[1:, :, None] * inputs[:-1, None, :]).sum(0)
E_xtp1_xutT = np.hstack((E_xtp1_xtT, E_xtp1_utT))
def is_symmetric(A):
return np.allclose(A, A.T)
assert is_symmetric(E_xt_xtT)
assert is_symmetric(E_xtp1_xtp1T)
self.E_dynamics_stats = np.array(
[E_xtp1_xtp1T, E_xtp1_xutT, E_xut_xutT, self.T - 1])
# Emission statistics
E_ysq = np.sum(data**2 * mask, axis=0)
E_yxT = (data * mask).T.dot(smoothed_mus)
E_yuT = (data * mask).T.dot(inputs)
E_yxuT = np.hstack((E_yxT, E_yuT))
E_xuxuT_vec = E_xu_xuT.reshape((T, -1))
E_xuxuT = np.array([
np.dot(self.mask[:, i], E_xuxuT_vec).reshape((n + d, n + d))
for i in range(p)
])
Tp = np.sum(self.mask, axis=0)
self.E_emission_stats = objarray([E_ysq, E_yxuT, E_xuxuT, Tp])
def _set_expected_stats(self, smoothed_mus, smoothed_sigmas, E_xtp1_xtT):
# Get the emission stats
p, n, d, T, inputs, data = \
self.D_emission, self.D_latent, self.D_input, self.T, \
self.inputs, self.data
E_x_xT = smoothed_sigmas + self.smoothed_mus[:, :,
None] * self.smoothed_mus[:,
None, :]
E_x_uT = smoothed_mus[:, :, None] * self.inputs[:, None, :]
E_u_uT = self.inputs[:, :, None] * self.inputs[:, None, :]
E_xu_xuT = np.concatenate(
(np.concatenate((E_x_xT, E_x_uT), axis=2),
np.concatenate((np.transpose(E_x_uT,
(0, 2, 1)), E_u_uT), axis=2)),
axis=1)
E_xut_xutT = E_xu_xuT[:-1].sum(0)
E_xtp1_xtp1T = E_x_xT[1:].sum(0)
E_xtp1_xtT = E_xtp1_xtT.sum(0)
E_xtp1_utT = (smoothed_mus[1:, :, None] * inputs[:-1, None, :]).sum(0)
E_xtp1_xutT = np.hstack((E_xtp1_xtT, E_xtp1_utT))
# def is_symmetric(A):
# return np.allclose(A, A.T)
# assert is_symmetric(E_xt_xtT)
# assert is_symmetric(E_xtp1_xtp1T)
self.E_dynamics_stats = np.array(
[E_xtp1_xtp1T, E_xtp1_xutT, E_xut_xutT, self.T - 1])
# Emission statistics
E_yyT = np.sum(data**2,
axis=0) if self.diagonal_noise else data.T.dot(data)
E_yxT = data.T.dot(smoothed_mus)
E_yuT = data.T.dot(inputs)
E_yxuT = np.hstack((E_yxT, E_yuT))
self.E_emission_stats = objarray([E_yyT, E_yxuT, E_xu_xuT.sum(0), T])
def _null_stats(self):
return objarray(
[np.zeros(self.D_obs),
np.zeros((self.D_obs, self.D_latent)),
np.zeros((self.D_obs, self.D_latent, self.D_latent)),
np.zeros(self.D_obs)])
