JOINT STOCHASTIC APPROXIMATION LEARNING OF HELMHOLTZ MACHINES
Authors: Haotian Xu, Zhijian Ou

Abstract: Though with progress, model learning and performing posterior inference still re-
mains a common challenge for using deep generative models, especially for han-
dling discrete hidden variables. This paper is mainly concerned with algorithms
for learning Helmholz machines, which is characterized by pairing the genera-
tive model with an auxiliary inference model. A common drawback of previous
learning algorithms is that they indirectly optimize some bounds of the targeted
marginal log-likelihood. In contrast, we successfully develop a new class of al-
gorithms, based on stochastic approximation (SA) theory of the Robbins-Monro
type, to directly optimize the marginal log-likelihood and simultaneously mini-
mize the inclusive KL-divergence. The resulting learning algorithm is thus called
joint SA (JSA). Moreover, we construct an effective MCMC operator for JSA. Our
results on the MNIST datasets demonstrate that the JSA’s performance is consis-
tently superior to that of competing algorithms like RWS, for learning a range of
difficult models.