def kl_divergence(self, q_X, q_A, _):
# q_Xt - [N, H, ds]
# q_At - [N, H, da]
if (q_X, q_A) not in self.cache:
q_Xt = q_X.__class__([
q_X.get_parameters('regular')[0][:, :-1],
q_X.get_parameters('regular')[1][:, :-1],
])
q_At = q_A.__class__([
q_A.get_parameters('regular')[0][:, :-1],
q_A.get_parameters('regular')[1][:, :-1],
])
p_Xt1 = self.forward(q_Xt, q_At)
q_Xt1 = q_X.__class__([
q_X.get_parameters('regular')[0][:, 1:],
q_X.get_parameters('regular')[1][:, 1:],
])
rmse = T.sqrt(
T.sum(T.square(
q_Xt1.get_parameters('regular')[1] -
p_Xt1.get_parameters('regular')[1]),
axis=-1))
model_stdev = T.sqrt(p_Xt1.get_parameters('regular')[0])
encoding_stdev = T.sqrt(q_Xt1.get_parameters('regular')[0])
self.cache[(q_X, q_A)] = T.sum(stats.kl_divergence(q_Xt1, p_Xt1),
axis=-1), {
'rmse': rmse,
'encoding-stdev':
encoding_stdev,
'model-stdev': model_stdev
}
return self.cache[(q_X, q_A)]
def kl_divergence(self, q_X, q_A, _):
# q_Xt - [N, H, ds]
# q_At - [N, H, da]
if (q_X, q_A) not in self.cache:
info = {}
if self.smooth:
state_prior = stats.GaussianScaleDiag([
T.ones(self.ds),
T.zeros(self.ds)
])
p_X = stats.LDS(
(self.sufficient_statistics(), state_prior, None, q_A.expected_value(), self.horizon),
'internal')
kl = T.mean(stats.kl_divergence(q_X, p_X), axis=0)
Q = self.get_dynamics()[1]
info['model-stdev'] = T.sqrt(T.matrix_diag_part(Q))
else:
q_Xt = q_X.__class__([
q_X.get_parameters('regular')[0][:, :-1],
q_X.get_parameters('regular')[1][:, :-1],
])
q_At = q_A.__class__([
q_A.get_parameters('regular')[0][:, :-1],
q_A.get_parameters('regular')[1][:, :-1],
])
p_Xt1 = self.forward(q_Xt, q_At)
q_Xt1 = q_X.__class__([
q_X.get_parameters('regular')[0][:, 1:],
q_X.get_parameters('regular')[1][:, 1:],
])
rmse = T.sqrt(T.sum(T.square(q_Xt1.get_parameters('regular')[1] - p_Xt1.get_parameters('regular')[1]), axis=-1))
kl = T.mean(T.sum(stats.kl_divergence(q_Xt1, p_Xt1), axis=-1), axis=0)
Q = self.get_dynamics()[1]
model_stdev = T.sqrt(T.matrix_diag_part(Q))
info['rmse'] = rmse
info['model-stdev'] = model_stdev
self.cache[(q_X, q_A)] = kl, info
return self.cache[(q_X, q_A)]
def kl_divergence(self, q_X, q_A, num_data):
if (q_X, q_A) not in self.cache:
if self.smooth:
state_prior = stats.GaussianScaleDiag(
[T.ones(self.ds), T.zeros(self.ds)])
self.p_X = stats.LDS(
(self.sufficient_statistics(), state_prior, None,
q_A.expected_value(), self.horizon), 'internal')
local_kl = stats.kl_divergence(q_X, self.p_X)
if self.time_varying:
global_kl = T.sum(
stats.kl_divergence(self.A_variational, self.A_prior))
else:
global_kl = stats.kl_divergence(self.A_variational,
self.A_prior)
prior_kl = T.mean(local_kl,
axis=0) + global_kl / T.to_float(num_data)
A, Q = self.get_dynamics()
model_stdev = T.sqrt(T.matrix_diag_part(Q))
self.cache[(q_X, q_A)] = prior_kl, {
'local-kl': local_kl,
'global-kl': global_kl,
'model-stdev': model_stdev,
}
else:
q_Xt = q_X.__class__([
q_X.get_parameters('regular')[0][:, :-1],
q_X.get_parameters('regular')[1][:, :-1],
])
q_At = q_A.__class__([
q_A.get_parameters('regular')[0][:, :-1],
q_A.get_parameters('regular')[1][:, :-1],
])
p_Xt1 = self.forward(q_Xt, q_At)
q_Xt1 = q_X.__class__([
q_X.get_parameters('regular')[0][:, 1:],
q_X.get_parameters('regular')[1][:, 1:],
])
num_data = T.to_float(num_data)
rmse = T.sqrt(
T.sum(T.square(
q_Xt1.get_parameters('regular')[1] -
p_Xt1.get_parameters('regular')[1]),
axis=-1))
A, Q = self.get_dynamics()
model_stdev = T.sqrt(T.matrix_diag_part(Q))
local_kl = T.sum(stats.kl_divergence(q_Xt1, p_Xt1), axis=1)
if self.time_varying:
global_kl = T.sum(
stats.kl_divergence(self.A_variational, self.A_prior))
else:
global_kl = stats.kl_divergence(self.A_variational,
self.A_prior)
self.cache[(q_X, q_A)] = (T.mean(local_kl, axis=0) +
global_kl / T.to_float(num_data), {
'rmse': rmse,
'model-stdev': model_stdev,
'local-kl': local_kl,
'global-kl': global_kl
})
return self.cache[(q_X, q_A)]
def log_likelihood(self, batch_z, batch):
x = Vector(self.input_size, placeholder=batch, is_input=False)
mu, sigma = (x >> self.q_network).get_graph_outputs()
sigma = T.sqrt(T.exp(sigma))
return T.mean(
log_normal(batch_z, mu, sigma, self.embedding_size, dim=2))
def sample_z(self, batch, batch_noise, feed_dict={}):
x = Vector(self.input_size, placeholder=batch, is_input=False)
mu, sigma = (x >> self.q_network).get_graph_outputs()
sigma = T.sqrt(T.exp(sigma))
return mu + sigma * batch_noise