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Auxiliary variable transformations for intractable distributions Vanetti, Paul Justin Cesare
Abstract
Expectations over probability distributions can be approximated by Markov chain Monte Carlo methods when the density can be evaluated up to a normalizing constant. However, there exist cases where this density takes on the form of an intractable integral and therefore cannot be computed exactly. We explore a class of auxiliary variable methods which allow correct sampling from such distributions. In some cases, existing approaches which employ these methods can be inefficient, requiring long computation times. We identify causes for this inefficiency and demonstrate how this can be improved when we can develop a reasonable importance sampling estimate of the integral. We discuss applications for our methods, placing a particular focus on the Dirichlet process with a non-conjugate base distribution. We show how the auxiliary variables can be interpreted in this non-parametric context, and how we can develop proposals which provide greater computational efficiency.
Item Metadata
Title |
Auxiliary variable transformations for intractable distributions
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2013
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Description |
Expectations over probability distributions can be approximated by Markov chain Monte Carlo methods when the density can be evaluated up to a normalizing constant. However, there exist cases where this density takes on the form of an intractable integral and therefore cannot be computed exactly. We explore a class of auxiliary variable methods which allow correct sampling from such distributions. In some cases, existing approaches which employ these methods can be inefficient, requiring long computation times. We identify causes for this inefficiency and demonstrate how this can be improved when we can develop a reasonable importance sampling estimate of the integral. We discuss applications for our methods, placing a particular focus on the Dirichlet process with a non-conjugate base distribution. We show how the auxiliary variables can be interpreted in this non-parametric context, and how we can develop proposals which provide greater computational efficiency.
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Genre | |
Type | |
Language |
eng
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Date Available |
2013-04-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0052200
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2013-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International