Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood
This work addresses a specific problem in probabilistic graphical modeling for researchers, offering an incremental improvement in structure learning methods.
The authors tackled the challenge of structure learning for contextual Markov networks, which model context-specific independences, by introducing the marginal pseudo-likelihood as a tractable criterion, resulting in a consistent estimator with improved predictive accuracy in experiments.
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov networks have been proposed. Here we consider the class of contextual Markov networks which takes into account possible context-specific independences among pairs of variables. Structure learning of contextual Markov networks is very challenging due to the extremely large number of possible structures. One of the main challenges has been to design a score, by which a structure can be assessed in terms of model fit related to complexity, without assuming chordality. Here we introduce the marginal pseudo-likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator. Experiments demonstrate the favorable properties of our method in terms of predictive accuracy of the inferred models.