Learning discrete decomposable graphical models via constraint optimization

Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be successful in proving the global optimality of solutions, in contrast to stochastic algorithms that only guarantee optimality at the limit. Here we improve and generalize a recently introduced constraint-based method for learning undirected graphical models. The new method combines perfect elimination orderings with various strategies for solution pruning B Jukka Corander [email protected] Tomi Janhunen [email protected] Martin Gebser [email protected] Jussi Rintanen [email protected] Henrik Nyman [email protected] Johan Pensar [email protected] 1 Department of Computer Science, Aalto University, Espoo, Finland 2 University of Potsdam, Potsdam, Germany 3 Griffith University, Brisbane, Australia 4 Department of Mathematics and Statistics, Åbo Akademi University, Åbo, Finland 5 Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland and offers a dramatic improvement both in terms of time and memory complexity. We also show that the method is capable of efficiently handling a more general class of models, called stratified/labeled graphical models, which have an astronomically larger model space.