Estimating the partition function by discriminance sampling
Qiang Liu, Jian Xun Peng, Alexander Ihler, John W. Fisher · 2015
Importance sampling (IS) and its variant, an-nealed IS (AIS) have been widely used for es-timating the partition function in graphical mod-els, such as Markov random fields and deep gen-erative models. However, IS tends to underesti-mate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, “reverse ” versions of IS and AIS tend to overestimate the partition function, and degener-ate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the pro-posal. We give extensive theoretical and empir-ical justification; in particular, we show that an annealed version of our method significantly out-performs both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the state-of-the-art for likelihood evaluation in deep gen-erative models. 1