Article ID Journal Published Year Pages File Type
977252 Physica A: Statistical Mechanics and its Applications 2006 13 Pages PDF
Abstract

When we consider a problem in information processing, it is convenient to formulate the problem by using a random Ising model in statistical physics. However, a kind of computational difficulty arises in a case that the number of nodes becomes large. Hence approximation schemes such as a mean field approximation and a Bethe approximation have been used extensively for overcoming the difficulty. When frustration is essential in some problems, the Bethe approximation gives unfavorable results. In those problems, more advanced approximation schemes are needed beyond the Bethe approximation. In the present paper, we present explicitly the triangular approximation, which is the next approximation to the Bethe approximation. We apply the obtained approximation scheme to a Boltzmann machine in order to investigate the validity of the triangular approximation.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
Authors
, ,