Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields

Probabilistic graphical models for continuous variables can be built out of either parametric or nonparametric conditional density estimators. While several research efforts have been focusing on parametric approaches (such as Gaussian models), kernel-based estimators are still the only viable and wellunderstood option for nonparametric density estimation. This paper develops a semiparametric estimator of probability density functions based on the nonparanormal transformation, which has been recently proposed for mapping arbitrarily distributed data samples onto normally distributed datasets. Pointwise and uniform consistency properties are established for the developed method. The resulting density model is then applied to pseudo-likelihood estimation in Markov random fields. An experimental evaluation on data distributed according to a variety of density functions indicates that such semiparametric Markov random field models significantly outperform both their Gaussian and kernel-based alternatives in terms of prediction accuracy.