title: The high-order Boltzmann machine: learned distribution and topology.
abstract: In this paper we give a formal definition of the high-order Boltzmann machine (BM), and extend the well-known results on the convergence of the learning algorithm of the two-order BM. From the Bahadur-Lazarsfeld expansion we characterize the probability distribution learned by the high order BM. Likewise a criterion is given to establish the topology of the BM depending on the significant correlations of the particular probability distribution to be learned.
authors.affiliation: Dept. of Comput. Sci. and Artificial Intelligence, Univ. of the Basque Country, San Sebastian.
authors.forename: F X
authors.initials: FX
authors.lastname: Albizuri
authors.forename: A
authors.initials: A
authors.lastname: Danjou
authors.forename: M
authors.initials: M
authors.lastname: Grana
authors.forename: J
authors.initials: J
authors.lastname: Torrealdea
authors.forename: M C
authors.initials: MC
authors.lastname: Hernandez