Minimum conditional description length estimation for Markov random fields

In this paper we discuss a method, which we call Minimum Conditional Description Length (MCDL), for estimating the parameters of a subset of sites within a Markov random field. We assume that the edges are known for the entire graph G = (V, E). Then, for a subset U ⊂ V, we estimate the parameters for nodes in U as well as for edges incident to a node in U, by finding the exponential parameter for that subset that yields the best compression conditioned on the values on the boundary ∂U. Our estimate is derived from a temporally stationary sequence of observations on the set U. We discuss how this method can also be applied to estimate a spatially invariant parameter from a single configuration, and in so doing, derive the Maximum Pseudo-Likelihood (MPL) estimate.