def create_objectives_elbo(self, deterministic=False):
"""ELBO objective without the analytic expectation trick"""
# load network input
X = self.inputs[0]
x = X.flatten(2)
# load network output
if self.model == 'bernoulli':
q_mu, q_logsigma, p_mu, z \
= lasagne.layers.get_output(self.network[2:], deterministic=deterministic)
elif self.model == 'gaussian':
raise NotImplementedError()
# entropy term
log_qz_given_x = log_normal2(z, q_mu, q_logsigma).sum(axis=1)
# expected p(x,z) term
z_prior_sigma = T.cast(T.ones_like(q_logsigma),
dtype=theano.config.floatX)
z_prior_mu = T.cast(T.zeros_like(q_mu), dtype=theano.config.floatX)
log_pz = log_normal(z, z_prior_mu, z_prior_sigma).sum(axis=1)
log_px_given_z = log_bernoulli(x, p_mu).sum(axis=1)
log_pxz = log_pz + log_px_given_z
elbo = (log_pxz - log_qz_given_x).mean()
# we don't use the spearate accuracy metric right now
return -elbo, -log_qz_given_x.mean()
def create_objectives(self, deterministic=False):
# load network input
X = self.inputs[0]
x = X.flatten(2)
# duplicate entries to take into account multiple mc samples
n_sam = self.n_sample
n_out = x.shape[1]
x = x.dimshuffle(0, 'x', 1).repeat(n_sam, axis=1).reshape((-1, n_out))
# load network
l_px_mu, l_px_logsigma, l_pa_mu, l_pa_logsigma, \
l_qz_mu, l_qz_logsigma, l_qa_mu, l_qa_logsigma, \
l_qa, l_qz = self.network
# load network output
pa_mu, pa_logsigma, qz_mu, qz_logsigma, qa_mu, qa_logsigma, a, z \
= lasagne.layers.get_output(
[ l_pa_mu, l_pa_logsigma, l_qz_mu, l_qz_logsigma,
l_qa_mu, l_qa_logsigma, l_qa, l_qz ],
deterministic=deterministic)
if self.model == 'bernoulli':
px_mu = lasagne.layers.get_output(l_px_mu,
deterministic=deterministic)
elif self.model == 'gaussian':
px_mu, px_logsigma = lasagne.layers.get_output(
[l_px_mu, l_px_logsigma], deterministic=deterministic)
# entropy term
log_qa_given_x = log_normal2(a, qa_mu, qa_logsigma).sum(axis=1)
log_qz_given_ax = log_normal2(z, qz_mu, qz_logsigma).sum(axis=1)
log_qza_given_x = log_qz_given_ax + log_qa_given_x
# log-probability term
z_prior_sigma = T.cast(T.ones_like(qz_logsigma),
dtype=theano.config.floatX)
z_prior_mu = T.cast(T.zeros_like(qz_mu), dtype=theano.config.floatX)
log_pz = log_normal(z, z_prior_mu, z_prior_sigma).sum(axis=1)
log_pa_given_z = log_normal2(a, pa_mu, pa_logsigma).sum(axis=1)
if self.model == 'bernoulli':
log_px_given_z = log_bernoulli(x, px_mu).sum(axis=1)
elif self.model == 'gaussian':
log_px_given_z = log_normal2(x, px_mu, px_logsigma).sum(axis=1)
log_paxz = log_pa_given_z + log_px_given_z + log_pz
# # experiment: uniform prior p(a)
# a_prior_sigma = T.cast(T.ones_like(qa_logsigma), dtype=theano.config.floatX)
# a_prior_mu = T.cast(T.zeros_like(qa_mu), dtype=theano.config.floatX)
# log_pa = log_normal(a, a_prior_mu, a_prior_sigma).sum(axis=1)
# log_paxz = log_pa + log_px_given_z + log_pz
# compute the evidence lower bound
elbo = T.mean(log_paxz - log_qza_given_x)
# we don't use a spearate accuracy metric right now
return -elbo, T.max(qz_logsigma)
def create_gradients(self, loss, deterministic=False):
from theano.gradient import disconnected_grad as dg
# load network input
X = self.inputs[0]
x = X.flatten(2)
# load network output
if self.model == 'bernoulli':
q_mu, q_logsigma, p_mu, z \
= lasagne.layers.get_output(self.network[2:], deterministic=deterministic)
elif self.model == 'gaussian':
raise NotImplementedError()
# load params
p_params, q_params = self._get_net_params()
# entropy term
log_qz_given_x = log_normal2(z, q_mu, q_logsigma).sum(axis=1)
# expected p(x,z) term
z_prior_sigma = T.cast(T.ones_like(q_logsigma),
dtype=theano.config.floatX)
z_prior_mu = T.cast(T.zeros_like(q_mu), dtype=theano.config.floatX)
log_pz = log_normal(z, z_prior_mu, z_prior_sigma).sum(axis=1)
log_px_given_z = log_bernoulli(x, p_mu).sum(axis=1)
log_pxz = log_pz + log_px_given_z
# compute learning signals
l = log_pxz - log_qz_given_x
# l_avg, l_std = l.mean(), T.maximum(1, l.std())
# c_new = 0.8*c + 0.2*l_avg
# v_new = 0.8*v + 0.2*l_std
# l = (l - c_new) / v_new
# compute grad wrt p
p_grads = T.grad(-log_pxz.mean(), p_params)
# compute grad wrt q
# q_target = T.mean(dg(l) * log_qz_given_x)
# q_grads = T.grad(-0.2*q_target, q_params) # 5x slower rate for q
log_qz_given_x = log_normal2(dg(z), q_mu, q_logsigma).sum(axis=1)
q_target = T.mean(dg(l) * log_qz_given_x)
q_grads = T.grad(-0.2 * q_target, q_params) # 5x slower rate for q
# q_grads = T.grad(-l.mean(), q_params) # 5x slower rate for q
# # compute grad of cv net
# cv_target = T.mean(l**2)
# cv_grads = T.grad(cv_target, cv_params)
# combine and clip gradients
clip_grad = 1
max_norm = 5
grads = p_grads + q_grads
mgrads = lasagne.updates.total_norm_constraint(grads,
max_norm=max_norm)
cgrads = [T.clip(g, -clip_grad, clip_grad) for g in mgrads]
return cgrads
def _create_components(self, D):
# collect samples
(l_qx, l_qx_samp, l_pa_mu, l_pa_logsigma) = self.network
a = self.A
qx, x = lasagne.layers.get_output([l_qx, l_qx_samp], a)
pa_mu, pa_logsigma = lasagne.layers.get_output(
[l_pa_mu, l_pa_logsigma], x)
# compute logQ
logQa = T.sum(log_normal(a, 0., 1.), axis=1)
logQx_given_a = T.sum(log_bernoulli(x, qx), axis=1)
logQ = logQa + logQx_given_a
# compute energies of the samples, dim=(1, n_tot_samples)
logFx = self._free_energy(x.T, marginalize=self.marginalize)
logpa = T.sum(log_normal2(a, pa_mu, pa_logsigma), axis=1)
# logF = logFx + logpa
# free energy of the data
D = D.reshape((-1, self.n_visible)).T
logF_D = self._free_energy(D)
self._components = (logFx, logpa, logQ, logF_D)
def create_objectives(self, deterministic=False):
# load network input
X = self.inputs[0]
Y = self.inputs[1]
x = X.flatten(2)
# duplicate entries to take into account multiple mc samples
n_sam = self.n_sample
n_out = x.shape[1]
x = x.dimshuffle(0, 'x', 1).repeat(n_sam, axis=1).reshape((-1, n_out))
# load network
l_px_mu, l_px_logsigma, l_pa_mu, l_pa_logsigma, \
l_qz_mu, l_qz_logsigma, l_qa_mu, l_qa_logsigma, \
l_qa, l_qz, l_d = self.network
# load network output
pa_mu, pa_logsigma, qz_mu, qz_logsigma, qa_mu, qa_logsigma, a, z \
= lasagne.layers.get_output(
[ l_pa_mu, l_pa_logsigma, l_qz_mu, l_qz_logsigma,
l_qa_mu, l_qa_logsigma, l_qa, l_qz ],
deterministic=deterministic)
if self.model == 'bernoulli':
px_mu = lasagne.layers.get_output(l_px_mu,
deterministic=deterministic)
elif self.model == 'gaussian':
px_mu, px_logsigma = lasagne.layers.get_output(
[l_px_mu, l_px_logsigma], deterministic=deterministic)
# entropy term
log_qa_given_x = log_normal2(a, qa_mu, qa_logsigma).sum(axis=1)
log_qz_given_ax = log_normal2(z, qz_mu, qz_logsigma).sum(axis=1)
log_qza_given_x = log_qz_given_ax + log_qa_given_x
# log-probability term
z_prior_sigma = T.cast(T.ones_like(qz_logsigma),
dtype=theano.config.floatX)
z_prior_mu = T.cast(T.zeros_like(qz_mu), dtype=theano.config.floatX)
log_pz = log_normal(z, z_prior_mu, z_prior_sigma).sum(axis=1)
log_pa_given_z = log_normal2(a, pa_mu, pa_logsigma).sum(axis=1)
if self.model == 'bernoulli':
log_px_given_z = log_bernoulli(x, px_mu).sum(axis=1)
elif self.model == 'gaussian':
log_px_given_z = log_normal2(x, px_mu, px_logsigma).sum(axis=1)
log_paxz = log_pa_given_z + log_px_given_z + log_pz
# discriminative component
P = lasagne.layers.get_output(l_d)
P_test = lasagne.layers.get_output(l_d, deterministic=True)
disc_loss = lasagne.objectives.categorical_crossentropy(P, Y)
# measure accuracy
top = theano.tensor.argmax(P, axis=-1)
top_test = theano.tensor.argmax(P_test, axis=-1)
acc = theano.tensor.eq(top, Y).mean()
acc_test = theano.tensor.eq(top_test, Y).mean()
# compute the evidence lower bound
elbo = T.mean(-disc_loss + log_paxz - log_qza_given_x)
# elbo = T.mean(-disc_loss)
if deterministic:
return -elbo, acc_test
else:
return -elbo, acc