Statistical Manifolds, Self-Parallel Curves and Learning Processes
Guy Burdet, Ph. Combe, Hanna Nencka · Birkhäuser Basel eBooks · 1999
Introduced is some formalism of information geometry, new domain relating differential geometry to probability theory. Analysis and examinations of structure of some special spaces called statistical manifolds have been done. For the new geometry, covariant properties have been introduced. For that the new formalism the so-called α-geometry provides natural interpretation for the learning process, the learning rules have been discussed. The Boltzmann machine is studied using the previously described analysis of the manifold.