def map_fn(data):
data_shape = T.shape(data)
leading = data_shape[:-1]
dim_in = data_shape[-1]
flattened = T.reshape(data, [-1, dim_in])
net_out = network(flattened)
if isinstance(net_out, stats.GaussianScaleDiag):
scale_diag, mu = net_out.get_parameters('regular')
dim_out = T.shape(mu)[-1]
return stats.GaussianScaleDiag([
T.reshape(scale_diag, T.concatenate([leading, [dim_out]])),
T.reshape(mu, T.concatenate([leading, [dim_out]])),
])
elif isinstance(net_out, stats.Gaussian):
sigma, mu = net_out.get_parameters('regular')
dim_out = T.shape(mu)[-1]
return stats.Gaussian([
T.reshape(sigma, T.concatenate([leading, [dim_out, dim_out]])),
T.reshape(mu, T.concatenate([leading, [dim_out]])),
])
elif isinstance(net_out, stats.Bernoulli):
params = net_out.get_parameters('natural')
dim_out = T.shape(params)[-1]
return stats.Bernoulli(
T.reshape(params, T.concatenate([leading, [dim_out]])),
'natural')
else:
raise Exception("Unimplemented distribution")
def initialize_node(node, children):
if isinstance(node, Gaussian):
d = T.shape(node)
return Gaussian([T.eye(d[-1], batch_shape=d[:-1]), T.random_normal(d)])
elif isinstance(node, IW):
d = T.shape(node)
return IW([(T.to_float(d[-1]) + 1) * T.eye(d[-1], batch_shape=d[:-2]),
T.to_float(d[-1]) + 1])
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 _sample(self, num_samples):
sigma, mu = self.natural_to_regular(self.regular_to_natural(self.get_parameters('regular')))
L = T.cholesky(sigma)
sample_shape = T.concat([[num_samples], T.shape(mu)], 0)
noise = T.random_normal(sample_shape)
L = T.tile(L[None], T.concat([[num_samples], T.ones([T.rank(sigma)], dtype=np.int32)]))
return mu[None] + T.matmul(L, noise[..., None])[..., 0]
def next_state(self, state, action, t):
A, Q = self.get_dynamics()
leading_dim = T.shape(state)[:-1]
state_action = T.concatenate([state, action], -1)
return stats.Gaussian([
T.tile(Q[t][None], T.concatenate([leading_dim, [1, 1]])),
T.einsum('ab,nb->na', A[t], state_action)
])
def forward(self, q_Xt, q_At):
Xt, At = q_Xt.expected_value(), q_At.expected_value()
batch_size = T.shape(Xt)[0]
XAt = T.concatenate([Xt, At], -1)
A, Q = self.get_dynamics()
p_Xt1 = stats.Gaussian([
T.tile(Q[None], [batch_size, 1, 1, 1]),
T.einsum('nhs,hxs->nhx', XAt, A)
])
return p_Xt1
def __init__(self,
sensor_models,
calibration_model,
lr=1e-4,
batch_size=20,
log_dir=None,
**kwargs):
self.graph = T.core.Graph()
self.log_dir = log_dir
with self.graph.as_default():
self.calibration_model = calibration_model
self.board_ids = list(sensor_models.keys())
self.board_map = {b: i for i, b in enumerate(self.board_ids)}
self.sensor_map = sensor_models
self.sensor_models = [
sensor_models[board_id] for board_id in self.board_ids
]
self.architecture = pickle.dumps(
[sensor_models, calibration_model])
self.batch_size = batch_size
self.lr = lr
self.learning_rate = T.placeholder(T.floatx(), [])
self.sensors = T.placeholder(T.floatx(), [None, 3])
self.env = T.placeholder(T.floatx(), [None, 3])
self.board = T.placeholder(T.core.int32, [None])
self.boards = T.transpose(
T.pack([self.board,
T.range(T.shape(self.board)[0])]))
self.rep = T.gather_nd(
T.pack([
sensor_model(self.sensors)
for sensor_model in self.sensor_models
]), self.boards)
self.rep_ = T.placeholder(T.floatx(),
[None, self.rep.get_shape()[-1]])
rep_env = T.concat([self.rep, self.env], -1)
rep_env_ = T.concat([self.rep_, self.env], -1)
self.y_ = self.calibration_model(rep_env)
self.y_rep = self.calibration_model(rep_env_)
self.y = T.placeholder(T.floatx(), [None, 2])
self.loss = T.mean((self.y - self.y_)**2)
self.mae = T.mean(T.abs(self.y - self.y_))
T.core.summary.scalar('MSE', self.loss)
T.core.summary.scalar('MAE', self.mae)
self.summary = T.core.summary.merge_all()
self.train_op = T.core.train.AdamOptimizer(
self.learning_rate).minimize(self.loss)
self.session = T.interactive_session(graph=self.graph)
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), {}
D = 2
sigma = 0.5
sigma0 = 100
data = generate_data(N, D, K, sigma=sigma, sigma0=sigma0, seed=None)
p_pi = Dirichlet(T.constant(10.0 * np.ones([K], dtype=T.floatx())))
p_theta = NIW(
list(
map(lambda x: T.constant(np.array(x).astype(T.floatx())),
[np.eye(D) * sigma, np.zeros(D), 1, D + 1])))
prior = (p_pi, p_theta)
np.random.seed(None)
X = T.placeholder(T.floatx(), [None, D])
batch_size = T.shape(X)[0]
q_pi = make_variable(Dirichlet(np.ones([K], dtype=T.floatx())))
q_theta = make_variable(
NIW(
map(lambda x: np.array(x).astype(T.floatx()), [
np.tile(np.eye(D)[None] * 100, [K, 1, 1]),
np.random.multivariate_normal(
mean=np.zeros([D]), cov=np.eye(D) * 20, size=[K]),
np.ones(K),
np.ones(K) * (D + 1)
])))
sigma, mu = Gaussian(q_theta.expected_sufficient_statistics(),
parameter_type='natural').get_parameters('regular')
alpha = Categorical(q_pi.expected_sufficient_statistics(),
def posterior_dynamics(self,
q_X,
q_A,
data_strength=1.0,
max_iter=200,
tol=1e-3):
if self.smooth:
if self.time_varying:
prior_dyn = stats.MNIW(
self.A_variational.get_parameters('natural'), 'natural')
else:
natparam = self.A_variational.get_parameters('natural')
prior_dyn = stats.MNIW([
T.tile(natparam[0][None], [self.horizon - 1, 1, 1]),
T.tile(natparam[1][None], [self.horizon - 1, 1, 1]),
T.tile(natparam[2][None], [self.horizon - 1, 1, 1]),
T.tile(natparam[3][None], [self.horizon - 1]),
], 'natural')
state_prior = stats.Gaussian([T.eye(self.ds), T.zeros(self.ds)])
aaT, a = stats.Gaussian.unpack(
q_A.expected_sufficient_statistics())
aaT, a = aaT[:, :-1], a[:, :-1]
ds, da = self.ds, self.da
initial_dyn_natparam = prior_dyn.get_parameters('natural')
initial_X_natparam = stats.LDS(
(self.sufficient_statistics(), state_prior, q_X,
q_A.expected_value(), self.horizon),
'internal').get_parameters('natural')
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 cond(i, _, __, prev_elbo, curr_elbo):
with T.core.control_dependencies([T.core.print(curr_elbo)]):
prev_elbo = T.core.identity(prev_elbo)
return T.logical_and(
T.abs(curr_elbo - prev_elbo) > tol, i < max_iter)
result = T.while_loop(
cond,
em, [
0, initial_dyn_natparam, initial_X_natparam,
T.constant(-np.inf),
T.constant(0.)
],
back_prop=False)
pd = stats.MNIW(result[1], 'natural')
sigma, mu = pd.expected_value()
q_X = stats.LDS(result[2], 'natural')
return ((mu, sigma), pd.expected_sufficient_statistics()), (q_X,
q_A)
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],
])
q_Xt1 = q_X.__class__([
q_X.get_parameters('regular')[0][:, 1:],
q_X.get_parameters('regular')[1][:, 1:],
])
(XtAt_XtAtT, XtAt), (Xt1_Xt1T,
Xt1) = self.get_statistics(q_Xt, q_At, q_Xt1)
batch_size = T.shape(XtAt)[0]
ess = [
Xt1_Xt1T,
T.einsum('nha,nhb->nhba', XtAt, Xt1), XtAt_XtAtT,
T.ones([batch_size, self.horizon - 1])
]
if self.time_varying:
posterior = stats.MNIW([
T.sum(a, [0]) * data_strength + b for a, b in zip(
ess, self.A_variational.get_parameters('natural'))
], 'natural')
else:
posterior = stats.MNIW([
T.sum(a, [0]) * data_strength + b[None] for a, b in zip(
ess, self.A_variational.get_parameters('natural'))
], 'natural')
Q, A = posterior.expected_value()
return (A, Q), q_X
def shape(self):
return T.shape(Stats.X(self.m))
def shape(self):
return T.shape(self.value)
data = generate_data(1000)
N = data.shape[0]
yt, yt1 = data[:, :-1], data[:, 1:]
yt, yt1 = yt.reshape([-1, D]), yt1.reshape([-1, D])
transition_net = Tanh(D, 500) >> Tanh(500) >> nn.Gaussian(D)
transition_net.initialize()
rec_net = Tanh(D, 500) >> Tanh(500) >> nn.Gaussian(D)
rec_net.initialize()
Yt = T.placeholder(T.floatx(), [None, D])
Yt1 = T.placeholder(T.floatx(), [None, D])
batch_size = T.shape(Yt)[0]
num_batches = N / T.to_float(batch_size)
Yt_message = Gaussian.pack([
T.tile(T.eye(D)[None] * noise, [batch_size, 1, 1]),
T.einsum('ab,ib->ia',
T.eye(D) * noise, Yt)
])
Yt1_message = Gaussian.pack([
T.tile(T.eye(D)[None] * noise, [batch_size, 1, 1]),
T.einsum('ab,ib->ia',
T.eye(D) * noise, Yt1)
])
transition = Gaussian(transition_net(Yt)).expected_value()
max_iter = 1000
def initialize(self):
self.graph = T.core.Graph()
with self.graph.as_default():
prior_params = self.prior_params.copy()
prior_type = prior_params.pop('prior_type')
self.prior = PRIOR_MAP[prior_type](self.ds, self.da, self.horizon, **prior_params)
cost_params = self.cost_params.copy()
cost_type = cost_params.pop('cost_type')
self.cost = COST_MAP[cost_type](self.ds, self.da, **cost_params)
self.O = T.placeholder(T.floatx(), [None, None, self.do])
self.U = T.placeholder(T.floatx(), [None, None, self.du])
self.C = T.placeholder(T.floatx(), [None, None])
self.S = T.placeholder(T.floatx(), [None, None, self.ds])
self.A = T.placeholder(T.floatx(), [None, None, self.da])
self.t = T.placeholder(T.int32, [])
self.state, self.action = T.placeholder(T.floatx(), [None, self.ds]), T.placeholder(T.floatx(), [None, self.da])
if self.prior.has_dynamics():
self.next_state = self.prior.next_state(self.state, self.action, self.t)
self.prior_dynamics = self.prior.get_dynamics()
self.num_data = T.scalar()
self.beta = T.placeholder(T.floatx(), [])
self.learning_rate = T.placeholder(T.floatx(), [])
self.model_learning_rate = T.placeholder(T.floatx(), [])
self.S_potentials = util.map_network(self.state_encoder)(self.O)
self.A_potentials = util.map_network(self.action_encoder)(self.U)
if self.prior.is_dynamics_prior():
self.data_strength = T.placeholder(T.floatx(), [])
self.max_iter = T.placeholder(T.int32, [])
posterior_dynamics, (encodings, actions) = \
self.prior.posterior_dynamics(self.S_potentials, self.A_potentials,
data_strength=self.data_strength,
max_iter=self.max_iter)
self.posterior_dynamics_ = posterior_dynamics, (encodings.expected_value(), actions.expected_value())
if self.prior.is_filtering_prior():
self.prior_dynamics_stats = self.prior.sufficient_statistics()
self.dynamics_stats = (
T.placeholder(T.floatx(), [None, self.ds, self.ds]),
T.placeholder(T.floatx(), [None, self.ds, self.ds + self.da]),
T.placeholder(T.floatx(), [None, self.ds + self.da, self.ds + self.da]),
T.placeholder(T.floatx(), [None]),
)
S_natparam = self.S_potentials.get_parameters('natural')
num_steps = T.shape(S_natparam)[1]
self.padded_S = stats.Gaussian(T.core.pad(
self.S_potentials.get_parameters('natural'),
[[0, 0], [0, self.horizon - num_steps], [0, 0], [0, 0]]
), 'natural')
self.padded_A = stats.GaussianScaleDiag([
T.core.pad(self.A_potentials.get_parameters('regular')[0],
[[0, 0], [0, self.horizon - num_steps], [0, 0]]),
T.core.pad(self.A_potentials.get_parameters('regular')[1],
[[0, 0], [0, self.horizon - num_steps], [0, 0]])
], 'regular')
self.q_S_padded, self.q_A_padded = self.prior.encode(
self.padded_S, self.padded_A,
dynamics_stats=self.dynamics_stats
)
self.q_S_filter = self.q_S_padded.filter(max_steps=num_steps)
self.q_A_filter = self.q_A_padded.__class__(
self.q_A_padded.get_parameters('natural')[:, :num_steps]
, 'natural')
self.e_q_S_filter = self.q_S_filter.expected_value()
self.e_q_A_filter = self.q_A_filter.expected_value()
(self.q_S, self.q_A), self.prior_kl, self.kl_grads, self.info = self.prior.posterior_kl_grads(
self.S_potentials, self.A_potentials, self.num_data
)
self.q_S_sample = self.q_S.sample()[0]
self.q_A_sample = self.q_A.sample()[0]
self.q_O = util.map_network(self.state_decoder)(self.q_S_sample)
self.q_U = util.map_network(self.action_decoder)(self.q_A_sample)
self.q_O_sample = self.q_O.sample()[0]
self.q_U_sample = self.q_U.sample()[0]
self.q_O_ = util.map_network(self.state_decoder)(self.S)
self.q_U_ = util.map_network(self.action_decoder)(self.A)
self.q_O__sample = self.q_O_.sample()[0]
self.q_U__sample = self.q_U_.sample()[0]
self.cost_likelihood = self.cost.log_likelihood(self.q_S_sample, self.C)
if self.cost.is_cost_function():
self.evaluated_cost = self.cost.evaluate(self.S)
self.log_likelihood = T.sum(self.q_O.log_likelihood(self.O), axis=1)
self.elbo = T.mean(self.log_likelihood + self.cost_likelihood - self.prior_kl)
train_elbo = T.mean(self.log_likelihood + self.beta * (self.cost_likelihood - self.prior_kl))
T.core.summary.scalar("encoder-stdev", T.mean(self.S_potentials.get_parameters('regular')[0]))
T.core.summary.scalar("log-likelihood", T.mean(self.log_likelihood))
T.core.summary.scalar("cost-likelihood", T.mean(self.cost_likelihood))
T.core.summary.scalar("prior-kl", T.mean(self.prior_kl))
T.core.summary.scalar("beta", self.beta)
T.core.summary.scalar("elbo", self.elbo)
T.core.summary.scalar("beta-elbo", train_elbo)
for k, v in self.info.items():
T.core.summary.scalar(k, T.mean(v))
self.summary = T.core.summary.merge_all()
neural_params = (
self.state_encoder.get_parameters()
+ self.state_decoder.get_parameters()
+ self.action_encoder.get_parameters()
+ self.action_decoder.get_parameters()
)
cost_params = self.cost.get_parameters()
if len(neural_params) > 0:
optimizer = T.core.train.AdamOptimizer(self.learning_rate)
gradients, variables = zip(*optimizer.compute_gradients(-train_elbo, var_list=neural_params))
gradients, _ = tf.clip_by_global_norm(gradients, 5.0)
self.neural_op = optimizer.apply_gradients(zip(gradients, variables))
else:
self.neural_op = T.core.no_op()
if len(cost_params) > 0:
self.cost_op = T.core.train.AdamOptimizer(self.learning_rate).minimize(-self.elbo, var_list=cost_params)
else:
self.cost_op = T.core.no_op()
if len(self.kl_grads) > 0:
if self.prior.is_dynamics_prior():
# opt = lambda x: T.core.train.MomentumOptimizer(x, 0.5)
opt = lambda x: T.core.train.GradientDescentOptimizer(x)
else:
opt = T.core.train.AdamOptimizer
self.dynamics_op = opt(self.model_learning_rate).apply_gradients([
(b, a) for a, b in self.kl_grads
])
else:
self.dynamics_op = T.core.no_op()
self.train_op = T.core.group(self.neural_op, self.dynamics_op, self.cost_op)
self.session = T.interactive_session(graph=self.graph, allow_soft_placement=True, log_device_placement=False)
def activate(self, X):
shape = T.shape(X)
return stats.NIW.pack(
[T.outer(X, X), X,
T.ones(shape[:-1]),
T.ones(shape[:-1])])
def kl_gradients(self, q_X, q_A, _, num_data):
if self.smooth:
ds = self.ds
ess = q_X.expected_sufficient_statistics()
yyT = ess[..., :-1, ds:2 * ds, ds:2 * ds]
xxT = ess[..., :-1, :ds, :ds]
yxT = ess[..., :-1, ds:2 * ds, :ds]
aaT, a = stats.Gaussian.unpack(
q_A.expected_sufficient_statistics())
aaT, a = aaT[:, :-1], a[:, :-1]
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)
batch_size = T.shape(ess)[0]
num_batches = T.to_float(num_data) / T.to_float(batch_size)
ess = [
yyT,
T.concatenate([yxT, yaT], -1), xaxaT,
T.ones([batch_size, self.horizon - 1])
]
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],
])
q_Xt1 = q_X.__class__([
q_X.get_parameters('regular')[0][:, 1:],
q_X.get_parameters('regular')[1][:, 1:],
])
(XtAt_XtAtT, XtAt), (Xt1_Xt1T,
Xt1) = self.get_statistics(q_Xt, q_At, q_Xt1)
batch_size = T.shape(XtAt)[0]
num_batches = T.to_float(num_data) / T.to_float(batch_size)
ess = [
Xt1_Xt1T,
T.einsum('nha,nhb->nhba', XtAt, Xt1), XtAt_XtAtT,
T.ones([batch_size, self.horizon - 1])
]
if self.time_varying:
ess = [
T.sum(ess[0], [0]),
T.sum(ess[1], [0]),
T.sum(ess[2], [0]),
T.sum(ess[3], [0]),
]
else:
ess = [
T.sum(ess[0], [0, 1]),
T.sum(ess[1], [0, 1]),
T.sum(ess[2], [0, 1]),
T.sum(ess[3], [0, 1]),
]
return [
-(a + num_batches * b - c) / T.to_float(num_data)
for a, b, c in zip(
self.A_prior.get_parameters('natural'),
ess,
self.A_variational.get_parameters('natural'),
)
]
def kl_divergence(self, q_X, q_A, num_data):
batch_size = T.shape(q_X.expected_value())[0]
return T.zeros(batch_size), {}
def shape(self):
return T.shape(self.get_parameters('natural')[Stats.LogX])
(X, Y) = generate_data(N, D, seed=3)
cf = LogisticRegression(fit_intercept=False)
cf.fit(X, Y)
coef_ = cf.coef_
score_ = cf.score(X, Y)
q_w = make_variable(
Gaussian([T.to_float(np.eye(D))[None],
T.to_float(np.zeros(D))[None]]))
x, y = T.matrix(), T.vector()
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]