def _construct_compute_fe_terms(self):
"""
Construct theano function to compute the log-likelihood and posterior
KL-divergence terms for the variational free-energy.
"""
# setup some symbolic variables for theano to deal with
Xd = T.matrix()
Xc = T.zeros_like(Xd)
Xm = T.zeros_like(Xd)
# construct values to output
if self.x_type == 'bernoulli':
ll_term = log_prob_bernoulli(self.x, self.xg)
else:
ll_term = log_prob_gaussian2(self.x, self.xg, \
log_vars=self.bounded_logvar)
all_klds = gaussian_kld(self.q_z_given_x.output_mean, \
self.q_z_given_x.output_logvar, \
self.prior_mean, self.prior_logvar)
kld_term = T.sum(all_klds, axis=1)
# compile theano function for a one-sample free-energy estimate
fe_term_sample = theano.function(inputs=[Xd], \
outputs=[ll_term, kld_term], \
givens={self.Xd: Xd, self.Xc: Xc, self.Xm: Xm})
# construct a wrapper function for multi-sample free-energy estimate
def fe_term_estimator(X, sample_count):
ll_sum = np.zeros((X.shape[0],))
kld_sum = np.zeros((X.shape[0],))
for i in range(sample_count):
result = fe_term_sample(X)
ll_sum = ll_sum + result[0].ravel()
kld_sum = kld_sum + result[1].ravel()
mean_nll = -ll_sum / float(sample_count)
mean_kld = kld_sum / float(sample_count)
return [mean_nll, mean_kld]
return fe_term_estimator
def _construct_compute_fe_terms(self):
"""
Construct theano function to compute the log-likelihood and posterior
KL-divergence terms for the variational free-energy.
"""
# construct values to output
if self.x_type == 'bernoulli':
ll_term = log_prob_bernoulli(self.x_in, self.xg)
else:
ll_term = log_prob_gaussian2(self.x_in, self.xg, \
log_vars=self.bounded_logvar)
all_klds = gaussian_kld(self.z_mean, self.z_logvar, \
self.prior_mean, self.prior_logvar)
kld_term = T.sum(all_klds, axis=1)
# compile theano function for a one-sample free-energy estimate
fe_term_sample = theano.function(inputs=[self.x_in], \
outputs=[ll_term, kld_term])
# construct a wrapper function for multi-sample free-energy estimate
def fe_term_estimator(X, sample_count):
X = to_fX(X)
ll_sum = np.zeros((X.shape[0], ))
kld_sum = np.zeros((X.shape[0], ))
for i in range(sample_count):
result = fe_term_sample(X)
ll_sum = ll_sum + result[0].ravel()
kld_sum = kld_sum + result[1].ravel()
mean_nll = -ll_sum / float(sample_count)
mean_kld = kld_sum / float(sample_count)
return [mean_nll, mean_kld]
return fe_term_estimator
def _construct_compute_fe_terms(self):
"""
Construct theano function to compute the log-likelihood and posterior
KL-divergence terms for the variational free-energy.
"""
# construct values to output
if self.x_type == 'bernoulli':
ll_term = log_prob_bernoulli(self.x_in, self.xg)
else:
ll_term = log_prob_gaussian2(self.x_in, self.xg, \
log_vars=self.bounded_logvar)
all_klds = gaussian_kld(self.z_mean, self.z_logvar, \
self.prior_mean, self.prior_logvar)
kld_term = T.sum(all_klds, axis=1)
# compile theano function for a one-sample free-energy estimate
fe_term_sample = theano.function(inputs=[self.x_in], \
outputs=[ll_term, kld_term])
# construct a wrapper function for multi-sample free-energy estimate
def fe_term_estimator(X, sample_count):
X = to_fX(X)
ll_sum = np.zeros((X.shape[0],))
kld_sum = np.zeros((X.shape[0],))
for i in range(sample_count):
result = fe_term_sample(X)
ll_sum = ll_sum + result[0].ravel()
kld_sum = kld_sum + result[1].ravel()
mean_nll = -ll_sum / float(sample_count)
mean_kld = kld_sum / float(sample_count)
return [mean_nll, mean_kld]
return fe_term_estimator
def _log_prob_wrapper(self, x_true, x_apprx):
"""
Wrap log-prob with switching for bernoulli/gaussian output types.
"""
if self.x_type == 'bernoulli':
ll_cost = log_prob_bernoulli(x_true, x_apprx)
else:
ll_cost = log_prob_gaussian2(x_true, x_apprx, \
log_vars=self.bounded_logvar)
nll_cost = -ll_cost
return nll_cost
def _construct_nll_costs(self):
"""
Construct the negative log-likelihood part of cost to minimize.
"""
if self.x_type == 'bernoulli':
ll_cost = log_prob_bernoulli(self.x, self.xg)
else:
ll_cost = log_prob_gaussian2(self.x, self.xg, \
log_vars=self.bounded_logvar)
nll_cost = -ll_cost
return nll_cost
def _log_prob_wrapper(self, x_true, x_apprx):
"""
Wrap log-prob with switching for bernoulli/gaussian output types.
"""
if self.x_type == 'bernoulli':
ll_cost = log_prob_bernoulli(x_true, x_apprx)
else:
ll_cost = log_prob_gaussian2(x_true, x_apprx, \
log_vars=self.bounded_logvar)
nll_cost = -ll_cost
return nll_cost
def _construct_nll_costs(self):
"""
Construct the negative log-likelihood part of cost to minimize.
"""
if self.x_type == 'bernoulli':
ll_cost = log_prob_bernoulli(self.x, self.xg)
else:
ll_cost = log_prob_gaussian2(self.x, self.xg, \
log_vars=self.bounded_logvar)
nll_cost = -ll_cost
return nll_cost
def _construct_nll_costs(self, xo):
"""
Construct the negative log-likelihood part of free energy.
"""
# average log-likelihood over the refinement sequence
xh = self.obs_transform(self.x_gen)
if self.x_type == 'bernoulli':
ll_costs = log_prob_bernoulli(xo, xh)
else:
ll_costs = log_prob_gaussian2(xo, xh, log_vars=self.bounded_logvar)
nll_costs = -ll_costs
return nll_costs
def _construct_nll_costs(self, si, xo, nll_mask):
"""
Construct the negative log-likelihood part of free energy.
-- only check NLL where nll_mask == 1
"""
xh = self._from_si_to_x(si)
if self.x_type == "bernoulli":
ll_costs = log_prob_bernoulli(xo, xh, mask=nll_mask)
else:
ll_costs = log_prob_gaussian2(xo, xh, log_vars=self.bounded_logvar, mask=nll_mask)
nll_costs = -ll_costs.flatten()
return nll_costs
def compute_log_prob(self, Xd=None):
"""
Compute negative log likelihood of the data in Xd, with respect to the
output distributions currently at self.output_....
Compute log-prob for all entries in Xd.
"""
if (self.out_type == 'bernoulli'):
log_prob_cost = log_prob_bernoulli(Xd, self.output, mask=self.output_mask)
else:
log_prob_cost = log_prob_gaussian2(Xd, self.output_mu, \
les_logvars=self.output_logvar, mask=self.output_mask)
return log_prob_cost
def _construct_nll_costs(self, si, xo, nll_mask):
"""
Construct the negative log-likelihood part of free energy.
-- only check NLL where nll_mask == 1
"""
xh = self._from_si_to_x(si)
if self.x_type == 'bernoulli':
ll_costs = log_prob_bernoulli(xo, xh, mask=nll_mask)
else:
ll_costs = log_prob_gaussian2(xo, xh, \
log_vars=self.bounded_logvar, mask=nll_mask)
nll_costs = -ll_costs.flatten()
return nll_costs
def _construct_nll_costs(self, si, xo, xm):
"""
Construct the negative log-likelihood part of free energy.
"""
# average log-likelihood over the refinement sequence
xh = self._si_as_x(si)
xm_inv = 1.0 - xm # we will measure nll only where xm_inv is 1
if self.x_type == 'bernoulli':
ll_costs = log_prob_bernoulli(xo, xh, mask=xm_inv)
else:
ll_costs = log_prob_gaussian2(xo, xh, \
log_vars=self.bounded_logvar, mask=xm_inv)
nll_costs = -ll_costs.flatten()
return nll_costs
def _construct_nll_costs(self, si, xo, xm):
"""
Construct the negative log-likelihood part of free energy.
"""
# average log-likelihood over the refinement sequence
xh = self._si_as_x(si)
xm_inv = 1.0 - xm # we will measure nll only where xm_inv is 1
if self.x_type == 'bernoulli':
ll_costs = log_prob_bernoulli(xo, xh, mask=xm_inv)
else:
ll_costs = log_prob_gaussian2(xo, xh, \
log_vars=self.bounded_logvar, mask=xm_inv)
nll_costs = -ll_costs.flatten()
return nll_costs
def masked_log_prob(self, Xc=None, Xm=None):
"""
Compute negative log likelihood of the data in Xc, with respect to the
output distributions currently at self.output_....
Select entries in Xd to compute log-prob for based on the mask Xm. When
Xm[i] == 1, don't measure NLL Xc[i]...
"""
# to measure NLL for Xc[i] only when Xm[i] is 0, we need to make an
# inverse mask Xm_inv = 1 - X_m, because the masking in the log pdf
# functions measures NLL only for observations where the mask != 0.
Xm_inv = 1.0 - Xm
if (self.out_type == 'bernoulli'):
log_prob_cost = log_prob_bernoulli(Xc, self.output, mask=Xm_inv)
else:
log_prob_cost = log_prob_gaussian2(Xc, self.output_mu, \
les_logvars=self.output_logvar, mask=Xm_inv)
return log_prob_cost
def _construct_compute_fe_terms(self):
"""
Construct theano function to compute the log-likelihood and posterior
KL-divergence terms for the variational free-energy.
"""
# setup some symbolic variables for theano to deal with
Xd = T.matrix()
Xc = T.zeros_like(Xd)
Xm = T.zeros_like(Xd)
# construct values to output
if self.x_type == 'bernoulli':
ll_term = log_prob_bernoulli(self.x, self.xg)
else:
ll_term = log_prob_gaussian2(self.x, self.xg, \
log_vars=self.bounded_logvar)
all_klds = gaussian_kld(self.q_z_given_x.output_mean, \
self.q_z_given_x.output_logvar, \
self.prior_mean, self.prior_logvar)
kld_term = T.sum(all_klds, axis=1)
# compile theano function for a one-sample free-energy estimate
fe_term_sample = theano.function(inputs=[Xd], \
outputs=[ll_term, kld_term], \
givens={self.Xd: Xd, self.Xc: Xc, self.Xm: Xm})
# construct a wrapper function for multi-sample free-energy estimate
def fe_term_estimator(X, sample_count):
ll_sum = np.zeros((X.shape[0], ))
kld_sum = np.zeros((X.shape[0], ))
for i in range(sample_count):
result = fe_term_sample(X)
ll_sum = ll_sum + result[0].ravel()
kld_sum = kld_sum + result[1].ravel()
mean_nll = -ll_sum / float(sample_count)
mean_kld = kld_sum / float(sample_count)
return [mean_nll, mean_kld]
return fe_term_estimator
def __init__(self, rng=None, \
x_in=None, x_out=None, \
p_s0_given_z=None, \
p_hi_given_si=None, \
p_sip1_given_si_hi=None, \
q_z_given_x=None, \
q_hi_given_x_si=None, \
obs_dim=None, \
z_dim=None, h_dim=None, \
ir_steps=4, params=None, \
shared_param_dicts=None):
# setup a rng for this GIPair
self.rng = RandStream(rng.randint(100000))
# grab the user-provided parameters
self.params = params
self.x_type = self.params['x_type']
assert((self.x_type == 'bernoulli') or (self.x_type == 'gaussian'))
if 'obs_transform' in self.params:
assert((self.params['obs_transform'] == 'sigmoid') or \
(self.params['obs_transform'] == 'none'))
if self.params['obs_transform'] == 'sigmoid':
self.obs_transform = lambda x: T.nnet.sigmoid(20.0 * T.tanh(0.05 * x))
else:
self.obs_transform = lambda x: x
else:
self.obs_transform = lambda x: T.nnet.sigmoid(20.0 * T.tanh(0.05 * x))
if self.x_type == 'bernoulli':
self.obs_transform = lambda x: T.nnet.sigmoid(20.0 * T.tanh(0.05 * x))
self.shared_param_dicts = shared_param_dicts
# record the dimensions of various spaces relevant to this model
self.obs_dim = obs_dim
self.z_dim = z_dim
self.h_dim = h_dim
self.ir_steps = ir_steps
# grab handles to the relevant InfNets
self.q_z_given_x = q_z_given_x
self.q_hi_given_x_si = q_hi_given_x_si
self.p_s0_given_z = p_s0_given_z
self.p_hi_given_si = p_hi_given_si
self.p_sip1_given_si_hi = p_sip1_given_si_hi
# record the symbolic variables that will provide inputs to the
# computation graph created to describe this MultiStageModel
self.x_in = x_in
self.x_out = x_out
self.hi_zmuv = T.tensor3() # for ZMUV Gaussian samples to use in scan
# setup switching variable for changing between sampling/training
zero_ary = to_fX( np.zeros((1,)) )
self.train_switch = theano.shared(value=zero_ary, name='msm_train_switch')
self.set_train_switch(1.0)
# setup a variable for controlling dropout noise
self.drop_rate = theano.shared(value=zero_ary, name='msm_drop_rate')
self.set_drop_rate(0.0)
# this weight balances l1 vs. l2 penalty on posterior KLds
self.lam_kld_l1l2 = theano.shared(value=zero_ary, name='msm_lam_kld_l1l2')
self.set_lam_kld_l1l2(1.0)
if self.shared_param_dicts is None:
# initialize "optimizable" parameters specific to this MSM
init_vec = to_fX( np.zeros((self.z_dim,)) )
self.p_z_mean = theano.shared(value=init_vec, name='msm_p_z_mean')
self.p_z_logvar = theano.shared(value=init_vec, name='msm_p_z_logvar')
init_vec = to_fX( np.zeros((self.obs_dim,)) )
self.obs_logvar = theano.shared(value=zero_ary, name='msm_obs_logvar')
self.bounded_logvar = 8.0 * T.tanh((1.0/8.0) * self.obs_logvar)
self.shared_param_dicts = {}
self.shared_param_dicts['p_z_mean'] = self.p_z_mean
self.shared_param_dicts['p_z_logvar'] = self.p_z_logvar
self.shared_param_dicts['obs_logvar'] = self.obs_logvar
else:
self.p_z_mean = self.shared_param_dicts['p_z_mean']
self.p_z_logvar = self.shared_param_dicts['p_z_logvar']
self.obs_logvar = self.shared_param_dicts['obs_logvar']
self.bounded_logvar = 8.0 * T.tanh((1.0/8.0) * self.obs_logvar)
# setup a function for computing reconstruction log likelihood
if self.x_type == 'bernoulli':
self.log_prob_func = lambda xo, xh: \
(-1.0 * log_prob_bernoulli(xo, xh))
else:
self.log_prob_func = lambda xo, xh: \
(-1.0 * log_prob_gaussian2(xo, xh, \
log_vars=self.bounded_logvar))
# get a drop mask that drops things with probability p
drop_scale = 1. / (1. - self.drop_rate[0])
drop_rnd = self.rng.uniform(size=self.x_out.shape, \
low=0.0, high=1.0, dtype=theano.config.floatX)
drop_mask = drop_scale * (drop_rnd > self.drop_rate[0])
#############################
# Setup self.z and self.s0. #
#############################
print("Building MSM step 0...")
drop_x = drop_mask * self.x_in
self.q_z_mean, self.q_z_logvar, self.z = \
self.q_z_given_x.apply(drop_x, do_samples=True)
# get initial observation state
self.s0, _ = self.p_s0_given_z.apply(self.z, do_samples=False)
# gather KLd and NLL for the initialization step
self.init_klds = gaussian_kld(self.q_z_mean, self.q_z_logvar, \
self.p_z_mean, self.p_z_logvar)
self.init_nlls = -1.0 * \
self.log_prob_func(self.x_out, self.obs_transform(self.s0))
##################################################
# Setup the iterative generation loop using scan #
##################################################
def ir_step_func(hi_zmuv, sim1):
# get variables used throughout this refinement step
sim1_obs = self.obs_transform(sim1) # transform state -> obs
grad_ll = self.x_out - sim1_obs
# get samples of next hi, conditioned on current si
hi_p_mean, hi_p_logvar = self.p_hi_given_si.apply( \
sim1_obs, do_samples=False)
# now we build the model for variational hi given si
hi_q_mean, hi_q_logvar = self.q_hi_given_x_si.apply( \
T.horizontal_stack(grad_ll, sim1_obs), \
do_samples=False)
hi_q = (T.exp(0.5 * hi_q_logvar) * hi_zmuv) + hi_q_mean
hi_p = (T.exp(0.5 * hi_p_logvar) * hi_zmuv) + hi_p_mean
# make hi samples that can be switched between hi_p and hi_q
hi = ( ((self.train_switch[0] * hi_q) + \
((1.0 - self.train_switch[0]) * hi_p)) )
# p_sip1_given_si_hi is conditioned on si and hi.
ig_vals, fg_vals, in_vals = self.p_sip1_given_si_hi.apply(hi)
# get the transformed values (for an LSTM style update)
i_gate = 1.0 * T.nnet.sigmoid(ig_vals + 2.0)
f_gate = 1.0 * T.nnet.sigmoid(fg_vals + 2.0)
# perform an LSTM-like update of the state sim1 -> si
si = (in_vals * i_gate) + (sim1 * f_gate)
# compute generator NLL for this step
nlli = self.log_prob_func(self.x_out, self.obs_transform(si))
# compute relevant KLds for this step
kldi_q2p = gaussian_kld(hi_q_mean, hi_q_logvar, \
hi_p_mean, hi_p_logvar)
kldi_p2q = gaussian_kld(hi_p_mean, hi_p_logvar, \
hi_q_mean, hi_q_logvar)
return si, nlli, kldi_q2p, kldi_p2q
init_values = [self.s0, None, None, None]
self.scan_results, self.scan_updates = theano.scan(ir_step_func, \
outputs_info=init_values, sequences=self.hi_zmuv)
self.si = self.scan_results[0]
self.nlli = self.scan_results[1]
self.kldi_q2p = self.scan_results[2]
self.kldi_p2q = self.scan_results[3]
######################################################################
# ALL SYMBOLIC VARS NEEDED FOR THE OBJECTIVE SHOULD NOW BE AVAILABLE #
######################################################################
# shared var learning rate for generator and inferencer
zero_ary = to_fX( np.zeros((1,)) )
self.lr_1 = theano.shared(value=zero_ary, name='msm_lr_1')
self.lr_2 = theano.shared(value=zero_ary, name='msm_lr_2')
# shared var momentum parameters for generator and inferencer
self.mom_1 = theano.shared(value=zero_ary, name='msm_mom_1')
self.mom_2 = theano.shared(value=zero_ary, name='msm_mom_2')
# init parameters for controlling learning dynamics
self.set_sgd_params()
# init shared var for weighting nll of data given posterior sample
self.lam_nll = theano.shared(value=zero_ary, name='msm_lam_nll')
self.set_lam_nll(lam_nll=1.0)
# init shared var for weighting prior kld against reconstruction
self.lam_kld_z = theano.shared(value=zero_ary, name='msm_lam_kld_z')
self.lam_kld_q2p = theano.shared(value=zero_ary, name='msm_lam_kld_q2p')
self.lam_kld_p2q = theano.shared(value=zero_ary, name='msm_lam_kld_p2q')
self.set_lam_kld(lam_kld_z=1.0, lam_kld_q2p=0.7, lam_kld_p2q=0.3)
# init shared var for controlling l2 regularization on params
self.lam_l2w = theano.shared(value=zero_ary, name='msm_lam_l2w')
self.set_lam_l2w(1e-5)
# Grab all of the "optimizable" parameters in "group 1"
self.q_params = []
self.q_params.extend(self.q_z_given_x.mlp_params)
self.q_params.extend(self.q_hi_given_x_si.mlp_params)
# Grab all of the "optimizable" parameters in "group 2"
self.p_params = [self.p_z_mean, self.p_z_logvar]
self.p_params.extend(self.p_hi_given_si.mlp_params)
self.p_params.extend(self.p_sip1_given_si_hi.mlp_params)
self.p_params.extend(self.p_s0_given_z.mlp_params)
# Make a joint list of parameters group 1/2
self.joint_params = self.q_params + self.p_params
#################################
# CONSTRUCT THE KLD-BASED COSTS #
#################################
self.kld_z_q2p, self.kld_z_p2q, self.kld_hi_q2p, self.kld_hi_p2q = \
self._construct_kld_costs(p=1.0)
self.kld_z = (self.lam_kld_q2p[0] * self.kld_z_q2p) + \
(self.lam_kld_p2q[0] * self.kld_z_p2q)
self.kld_hi = (self.lam_kld_q2p[0] * self.kld_hi_q2p) + \
(self.lam_kld_p2q[0] * self.kld_hi_p2q)
self.kld_costs = (self.lam_kld_z[0] * self.kld_z) + self.kld_hi
# now do l2 KLd costs
self.kl2_z_q2p, self.kl2_z_p2q, self.kl2_hi_q2p, self.kl2_hi_p2q = \
self._construct_kld_costs(p=2.0)
self.kl2_z = (self.lam_kld_q2p[0] * self.kl2_z_q2p) + \
(self.lam_kld_p2q[0] * self.kl2_z_p2q)
self.kl2_hi = (self.lam_kld_q2p[0] * self.kl2_hi_q2p) + \
(self.lam_kld_p2q[0] * self.kl2_hi_p2q)
self.kl2_costs = (self.lam_kld_z[0] * self.kl2_z) + self.kl2_hi
# compute joint l1/l2 KLd cost
self.kld_l1l2_costs = (self.lam_kld_l1l2[0] * self.kld_costs) + \
((1.0 - self.lam_kld_l1l2[0]) * self.kl2_costs)
# compute "mean" (rather than per-input) costs
self.kld_cost = T.mean(self.kld_costs)
self.kl2_cost = T.mean(self.kl2_costs)
self.kld_l1l2_cost = T.mean(self.kld_l1l2_costs)
#################################
# CONSTRUCT THE NLL-BASED COSTS #
#################################
self.nll_costs = self.nlli[-1]
self.nll_cost = self.lam_nll[0] * T.mean(self.nll_costs)
########################################
# CONSTRUCT THE REST OF THE JOINT COST #
########################################
param_reg_cost = self._construct_reg_costs()
self.reg_cost = self.lam_l2w[0] * param_reg_cost
self.joint_cost = self.nll_cost + self.kld_l1l2_cost + \
self.reg_cost
##############################
# CONSTRUCT A PER-INPUT COST #
##############################
self.obs_costs = self.nll_costs + self.kld_l1l2_costs
# Get the gradient of the joint cost for all optimizable parameters
print("Computing gradients of self.joint_cost...")
self.joint_grads = OrderedDict()
grad_list = T.grad(self.joint_cost, self.joint_params)
for i, p in enumerate(self.joint_params):
self.joint_grads[p] = grad_list[i]
# Construct the updates for the generator and inferencer networks
self.q_updates = get_adam_updates(params=self.q_params, \
grads=self.joint_grads, alpha=self.lr_1, \
beta1=self.mom_1, beta2=self.mom_2, \
mom2_init=1e-3, smoothing=1e-5, max_grad_norm=10.0)
self.p_updates = get_adam_updates(params=self.p_params, \
grads=self.joint_grads, alpha=self.lr_2, \
beta1=self.mom_1, beta2=self.mom_2, \
mom2_init=1e-3, smoothing=1e-5, max_grad_norm=10.0)
self.joint_updates = OrderedDict()
for k in self.q_updates:
self.joint_updates[k] = self.q_updates[k]
for k in self.p_updates:
self.joint_updates[k] = self.p_updates[k]
# add scan updates, which seem to be required
for k in self.scan_updates:
self.joint_updates[k] = self.scan_updates[k]
# Construct a function for jointly training the generator/inferencer
print("Compiling cost computer...")
self.compute_raw_klds = self._construct_raw_klds()
print("Compiling training function...")
self.train_joint = self._construct_train_joint()
print("Compiling free-energy sampler...")
self.compute_fe_terms = self._construct_compute_fe_terms()
print("Compiling open-loop model sampler...")
self.sample_from_prior = self._construct_sample_from_prior()
print("Compiling data-guided model sampler...")
self.sample_from_input = self._construct_sample_from_input()
return