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Infinite-dimensional manifolds of finite-entropy probability measures

Newton, NJ (2013) Infinite-dimensional manifolds of finite-entropy probability measures. In: UNSPECIFIED, ? - ?.

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Abstract

This paper outlines recent work by the author on infinite-dimensional statistical manifolds, employing charts that are "balanced" between mixture and exponential representations. The manifolds are distinguished from one another by the exponent of the Lebesgue spaces (Lλ (μ), 2 ≤ λ < ∞) on which they are modelled. The α-divergences have mixed second-order partial derivatives on the manifolds, enabling the construction of the Fisher metric as a pseudo-Riemannian metric. This is enough for many applications; for example, it justifies projections of Markov processes onto submanifolds in recursive estimation problems. However, higher derivatives exist when the exponent λ is 3 or more, and this leads to a limited notion of α-connections on the tangent bundle. The manifolds are also natural objects in which to embed a variety of finite-dimensional statistical manifolds. © 2013 Springer-Verlag.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Additional Information: Published proceedings: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 23 Jul 2015 14:37
Last Modified: 27 Jun 2018 04:15
URI: http://repository.essex.ac.uk/id/eprint/14435

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