On Stochastic Estimation of Partition Function

TL;DR

This paper demonstrates how the duality in normal factor graphs can be exploited for stochastic estimation of partition functions, showing that primal and dual graph sampling perform differently depending on the temperature of the Potts model.

Contribution

It analytically and experimentally shows the benefits of using primal or dual NFG sampling for partition function estimation based on temperature regimes.

Findings

Primal NFG sampling is better at high temperatures.

Dual NFG sampling is better at low temperatures.

The duality approach improves estimation accuracy across temperature ranges.

Abstract

In this paper, we show analytically that the duality of normal factor graphs (NFG) can facilitate stochastic estimation of partition functions. In particular, our analysis suggests that for the $q-$ary two-dimensional nearest-neighbor Potts model, sampling from the primal NFG of the model and sampling from its dual exhibit opposite behaviours with respect to the temperature of the model. For high-temperature models, sampling from the primal NFG gives rise to better estimators whereas for low-temperature models, sampling from the dual gives rise to better estimators. This analysis is validated by experiments.