Probability Distributions from Riemannian Geometry, Generalized Hybrid Monte Carlo Sampling and Path Integrals

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Proceedings titleProceedings. IS and T/SPIE International Symposium on Electronic Imaging
ConferenceIS&T, SPIE International Symposium on Electronic Imaging , San Francisco, California, January 23-27, 2011
SubjectBayesian; Distribution; Euclidian; Geometry; Information Retrieval; Lagrangian; Monte Carlo; Path Integral; Riemannian
AbstractWhen considering probabilistic pattern recognition methods, especially methods based on Bayesian analysis, the probabilistic distribution is of the utmost importance. However, despite the fact that the geometry associated with the probability distribution constitutes essential background information, it is often not ascertained. This paper discusses how the standard Euclidian geometry should be generalized to the Riemannian geometry when a curvature is observed in the distribution. To this end, the probability distribution is defined for curved geometry. In order to calculate the probability distribution, a Lagrangian and a Hamiltonian constructed from curvature invariants are associated with the Riemannian geometry and a generalized hybrid Monte Carlo sampling is introduced. Finally, we consider the calculation of the probability distribution and the expectation in Riemannian space with path integrals, which allows a direct extension of the concept of probability to curved space.
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AffiliationNational Research Council Canada (NRC-CNRC); NRC Institute for Information Technology
Peer reviewedYes
NPARC number16512475
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Record identifier7f7a1018-88b9-4f92-be99-d7d8c0df9084
Record created2010-12-13
Record modified2016-05-10
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