def em(i, q_dyn_natparam, q_X_natparam, _, curr_elbo):
q_X_ = stats.LDS(q_X_natparam, 'natural')
ess = q_X_.expected_sufficient_statistics()
batch_size = T.shape(ess)[0]
yyT = ess[..., :-1, ds:2 * ds, ds:2 * ds]
xxT = ess[..., :-1, :ds, :ds]
yxT = ess[..., :-1, ds:2 * ds, :ds]
x = ess[..., :-1, -1, :ds]
y = ess[..., :-1, -1, ds:2 * ds]
xaT = T.outer(x, a)
yaT = T.outer(y, a)
xaxaT = T.concatenate([
T.concatenate([xxT, xaT], -1),
T.concatenate([T.matrix_transpose(xaT), aaT], -1),
], -2)
ess = [
yyT,
T.concatenate([yxT, yaT], -1), xaxaT,
T.ones([batch_size, self.horizon - 1])
]
q_dyn_natparam = [
T.sum(a, [0]) * data_strength + b
for a, b in zip(ess, initial_dyn_natparam)
]
q_dyn_ = stats.MNIW(q_dyn_natparam, 'natural')
q_stats = q_dyn_.expected_sufficient_statistics()
p_X = stats.LDS((q_stats, state_prior, None,
q_A.expected_value(), self.horizon))
q_X_ = stats.LDS((q_stats, state_prior, q_X,
q_A.expected_value(), self.horizon))
elbo = (T.sum(stats.kl_divergence(q_X_, p_X)) +
T.sum(stats.kl_divergence(q_dyn_, prior_dyn)))
return i + 1, q_dyn_.get_parameters(
'natural'), q_X_.get_parameters('natural'), curr_elbo, elbo
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 kl_divergence(self, q_X, q_A, num_data):
mu_shape = T.shape(q_X.get_parameters('regular')[1])
p_X = stats.GaussianScaleDiag([T.ones(mu_shape), T.zeros(mu_shape)])
return T.mean(T.sum(stats.kl_divergence(q_X, p_X), -1), 0), {}
x_stats = Gaussian.pack([
T.outer(X, X),
X,
])
theta_cmessage = q_theta.expected_sufficient_statistics()
num_batches = N / T.to_float(batch_size)
nat_scale = 10.0
parent_z = q_pi.expected_sufficient_statistics()[None]
new_z = T.einsum('iab,jab->ij', x_tmessage, theta_cmessage) + parent_z
q_z = Categorical(new_z - T.logsumexp(new_z, -1)[..., None],
parameter_type='natural')
p_z = Categorical(parent_z - T.logsumexp(parent_z, -1),
parameter_type='natural')
l_z = T.sum(kl_divergence(q_z, p_z))
z_pmessage = q_z.expected_sufficient_statistics()
pi_stats = T.sum(z_pmessage, 0)
parent_pi = p_pi.get_parameters('natural')
current_pi = q_pi.get_parameters('natural')
pi_gradient = nat_scale / N * (parent_pi + num_batches * pi_stats - current_pi)
l_pi = T.sum(kl_divergence(q_pi, p_pi))
theta_stats = T.einsum('ia,ibc->abc', z_pmessage, x_tmessage)
parent_theta = p_theta.get_parameters('natural')[None]
current_theta = q_theta.get_parameters('natural')
theta_gradient = nat_scale / N * (parent_theta + num_batches * theta_stats -
current_theta)
l_theta = T.sum(kl_divergence(q_theta, p_theta))
x_tmessage = NIW.pack([
T.outer(X, X),
X,
T.ones(N),
T.ones(N),
])
x_stats = Gaussian.pack([
T.outer(X, X),
X,
])
theta_cmessage = q_theta.expected_sufficient_statistics()
new_pi = p_pi.get_parameters('natural') + T.sum(z_pmessage, 0)
parent_pi = p_pi.get_parameters('natural')
pi_update = T.assign(q_pi.get_parameters('natural'), new_pi)
l_pi = T.sum(kl_divergence(q_pi, p_pi))
new_theta = T.einsum('ia,ibc->abc', z_pmessage,
x_tmessage) + p_theta.get_parameters('natural')[None]
parent_theta = p_theta.get_parameters('natural')
theta_update = T.assign(q_theta.get_parameters('natural'), new_theta)
l_theta = T.sum(kl_divergence(q_theta, p_theta))
parent_z = q_pi.expected_sufficient_statistics()[None]
new_z = T.einsum('iab,jab->ij', x_tmessage,
theta_cmessage) + q_pi.expected_sufficient_statistics()[None]
new_z = new_z - T.logsumexp(new_z, -1)[..., None]
z_update = T.assign(q_z.get_parameters('natural'), new_z)
l_z = T.sum(kl_divergence(q_z, Categorical(parent_z,
parameter_type='natural')))
# T.ones([batch_size]),
# T.ones([batch_size]),
# ])
# q_theta = make_variable(NIW(map(lambda x: np.array(x).astype(T.floatx()), [np.eye(D), np.random.multivariate_normal(mean=np.zeros([D]), cov=np.eye(D) * 20), 1.0, 1.0])))
num_batches = N / T.to_float(batch_size)
nat_scale = 1.0
theta_stats = T.sum(x_tmessage, 0)
parent_theta = p_theta.get_parameters('natural')
q_theta = NIW(parent_theta + theta_stats, parameter_type='natural')
sigma, mu = Gaussian(q_theta.expected_sufficient_statistics(),
parameter_type='natural').get_parameters('regular')
# theta_gradient = nat_scale / N * (parent_theta + num_batches * theta_stats - current_theta)
l_theta = T.sum(kl_divergence(q_theta, p_theta))
x_param = q_theta.expected_sufficient_statistics()[None]
q_x = Gaussian(T.tile(x_param, [batch_size, 1, 1]), parameter_type='natural')
l_x = T.sum(q_x.log_likelihood(X))
elbo = l_theta + l_x
elbos = []
l_thetas = []
l_xs = []
# natgrads = [(theta_gradient, q_theta.get_parameters('natural'))]
# nat_op = tf.group(*[T.assign(b, a + b) for a, b in natgrads])
# nat_opt = tf.train.GradientDescentOptimizer(1e-2)
# nat_op = nat_opt.apply_gradients([(-a, b) for a, b in natgrads])
lr = 1e-4
batch_size = T.shape(x)[0]
num_batches = T.to_float(N / batch_size)
with T.initialization('xavier'):
# stats_net = Relu(D + 1, 20) >> Relu(20) >> GaussianLayer(D)
stats_net = GaussianLayer(D + 1, D)
net_out = stats_net(T.concat([x, y[..., None]], -1))
stats = T.sum(net_out.get_parameters('natural'), 0)[None]
natural_gradient = (p_w.get_parameters('natural') + num_batches * stats -
q_w.get_parameters('natural')) / N
next_w = Gaussian(q_w.get_parameters('natural') + lr * natural_gradient,
parameter_type='natural')
l_w = kl_divergence(q_w, p_w)[0]
p_y = Bernoulli(T.sigmoid(T.einsum('jw,iw->ij', next_w.expected_value(), x)))
l_y = T.sum(p_y.log_likelihood(y[..., None]))
elbo = l_w + l_y
nat_op = T.assign(q_w.get_parameters('natural'),
next_w.get_parameters('natural'))
grad_op = tf.train.RMSPropOptimizer(1e-4).minimize(-elbo)
train_op = tf.group(nat_op, grad_op)
sess = T.interactive_session()
predictions = T.cast(
T.sigmoid(T.einsum('jw,iw->i', q_w.expected_value(), T.to_float(X))) + 0.5,
np.int32)
accuracy = T.mean(