ESTIMATION OF NETWORK STRUCTURES FROM PARTIALLY
OBSERVED MARKOV RANDOM FIELDS
YVES F. ATCHAD´E
Abstract. We consider the estimation of high-dimensional network structures from
partially observed Markov random field data using a penalized pseudo-likelihood ap-
proach. We fit a misspecified model obtained by ignoring the missing data problem. We
study the consistency of the estimator and derive a bound on its rate of convergence.
The results obtained relate the rate of convergence of the estimator to the extent of the
missing data problem. We report some simulation results that empirically validate some
of the theoretical findings.
1. Introduction and statement of the results
The problem of high-dimensional network structure estimation has recently attracted a
lot of attention in statistics and machine learning. Both in the continuous case using Gauss-
ian graphical models (Drton and Perlman (2004); Meinshausen and Buhlmann (2006);
Yuan and Lin (2007); d'Aspremont et al. (2008); Bickel and Levina (2008); Rothman et al.
(2008); Lam and Fan (2009)), and in the discrete case using Markov random fields (Banerjee et al.
(2008); H¨ofling and Tibshirani (2009); Ravikumar et al. (2010); Guo et al. (2010)). This
paper focuses mainly on Markov Random Fields (MRF) for non-Gaussian data. The prob-