Independence-Based MAP for Markov Networks Structure Discovery

Abstract

This work presents IBMAP, an approach for robust learning of Markov network structures from data, together with IBMAP-HC, an efficient instantiation of the approach. Existing Score-Based (SB) and Independence-Based (IB) approaches must make concessions either on robustness or efficiency. IBMAP-HC improves robustness efficiently through an IB-SB hybrid approach based on the probabilistic Maximum-A-Posteriori (MAP) technique, and the IB-score, a tractable expression for computing posterior probabilities of Markov network structures. Performance is first tested against IB and SB competitors on synthetic datasets. Against IB competitors (GSMN algorithm and a version of the HHC algorithm adapted here for Markov networks discovery), IBMAP-HC showed reductions in edges Hamming distance with same order running times. Against SB competitors, both IBMAP-HC and our adaptation of HHC produced comparable Hamming distances, but with running times orders of magnitude faster. We also evaluated IBMAP-HC in a realistic, challenging test-bed: EDAs, evolutionary algorithms for optimization that estimate a distribution on each generation. Using IBMAP-HC to estimate distributions, EDAs converged to the optimum faster in all benchmark functions considered, reducing required fitness evaluations by up to 80%.