Information Geometry and Mean Field Approximation: The α-projection Approach

Abstract

Information geometry is applied to mean field approximation for elucidating its properties in the spin glass model or the Boltzmann machine. The $α$-divergence is used for approximation, where $α$-geodesic projection plays an important role. The naive mean field approximation and TAP approximation are studied from the point of view of information geometry, which treats the intrinsic geometric structures of a family of probability distributions. The bifurcation of the $α$-projection is studied, at which the uniqueness of the $α$-approximation is broken.

Type
Publication
BSIS technical report