On the local and global properties of information manifolds

In the first part of the work, we show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor given its associated Nash embedding. We note further that this construction is extremely unconstrained, depending only on certain continuity properties of the probability density functions and a select symmetry of their domains. In the second part of the work, with the aim of understanding the global, algebrao-topological nature of information manifolds, we exhibit some of the necessary category theory required to effect a discussion of homological algebra in a general setting.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2015

Author dc:creator

• Clingman, Tslil

Advisor dc:contributor.advisor

• Murugan, Jeffrey

Language dc:language.iso

Eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/19950

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/19950