Fx. Albizuri et al., THE HIGH-ORDER BOLTZMANN MACHINE - LEARNED DISTRIBUTION AND TOPOLOGY, IEEE transactions on neural networks, 6(3), 1995, pp. 767-770
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.