Estimation of high-dimensional partially-observed discrete Markov random fields

Abstract

We consider the problem of estimating the parameters of discrete Markov random fields from partially observed data in a high-dimensional setting. Using a $\ell^{1}$-penalized pseudo-likelihood approach, we fit a misspecified model obtained by ignoring the missing data problem. We derive an estimation error bound that highlights the effect of the misspecification. We report some simulation results that illustrate the theoretical findings.