Transformation of Markov Random Fields for marginal distribution estimation

This paper presents a generic method for transforming MRFs for the marginal inference problem. Its major application is to downsize MRFs to speed up the computation. Unlike the MAP inference, there are only classical algorithms for the marginal inference problem such as BP etc. that require large computational cost. Although downsizing MRFs should directly reduce the computational cost, there is no systematic way of doing this, since it is unclear how to obtain the MRF energy for the downsized MRFs and also how to translate the estimates of their marginal distributions to those of the original MRFs. The proposed method resolves these issues by a novel probabilistic formulation of MRF transformation. The key idea is to represent the joint distribution of an MRF with that of the transformed one, in which the variables of the latter are treated as latent variables. We also show that the proposed method can be applied to discretization of variable space of continuous MRFs and can be used with Markov chain Monte Carlo methods. The experimental results demonstrate the effectiveness of the proposed method.