Download | - View accepted manuscript: Probability Distributions from Riemannian Geometry, Generalized Hybrid Monte Carlo Sampling and Path Integrals (PDF, 841 KiB)
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DOI | Resolve DOI: https://doi.org/10.1117/12.872862 |
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Author | Search for: Paquet, Eric1; Search for: Viktor, Herna L. |
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Affiliation | - National Research Council of Canada. NRC Institute for Information Technology
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Format | Text, Article |
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Conference | IS&T, SPIE International Symposium on Electronic Imaging , San Francisco, California, January 23-27, 2011 |
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Subject | Bayesian; Distribution; Euclidian; Geometry; Information Retrieval; Lagrangian; Monte Carlo; Path Integral; Riemannian |
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Abstract | When 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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Publication date | 2011 |
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In | |
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Language | English |
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Peer reviewed | Yes |
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NPARC number | 16512475 |
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Export citation | Export as RIS |
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Report a correction | Report a correction (opens in a new tab) |
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Record identifier | 7f7a1018-88b9-4f92-be99-d7d8c0df9084 |
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Record created | 2010-12-13 |
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Record modified | 2020-06-04 |
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