THE HIGH-ORDER BOLTZMANN MACHINE - LEARNED DISTRIBUTION AND TOPOLOGY

Few theoretical and practical studies have been carried out on the hig h-order Boltzmann Machine (BM). In this paper we give a formal definit ion of the high-order BM, and we extend the well-known results on the convergence of the learning algorithm of the two-order BM. From the Ba hadur-Lazarsfeld expansion we characterize the probability distributio n learned by the high-order BM. Likewise a criterion is given to estab lish the topology of the BM depending on the significant correlations of the particular probability distribution to be learned.