A Generalization of Spatial Monte Carlo Integration

Spatial Monte Carlo integration (SMCI) is an extension of standard and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, superior results those from some existing methods. The approximation level be changed, it proved that a higher-order statistically more accurate than lower-order approximation. However, as proposed in the previous studies suffers limitation prevents application method dense systems. This study makes two different contributions follows. A generalization (called generalized (GSMCI)) proposed, which allows relaxation above-mentioned limitation; moreover, statistical accuracy bound GSMCI proved. first contribution this study. new PBM learning based obtained by combining persistent contrastive divergence. greatly improves learning. second