Minimum Conditional Description Length Estimation for Markov Random Fields
This provides a parameter estimation method for Markov random fields, which is incremental as it builds on existing compression and likelihood techniques.
The paper tackles the problem of estimating parameters for a subset of sites in a Markov random field with known graph structure, proposing the Minimum Conditional Description Length (MCDL) method that finds parameters optimizing compression conditioned on boundary values, and shows it can derive the Maximum Pseudo-Likelihood estimate for spatially invariant parameters from a single configuration.
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 $U\subset V$, we estimate the parameters for nodes and edges 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 $\partial U$. 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.