Approximate variational inference based on a finite sample of Gaussian latent variables
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. margina...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
May 2016
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| In: |
Pattern analysis and applications
Year: 2016, Volume: 19, Issue: 2, Pages: 475-485 |
| ISSN: | 1433-755X |
| DOI: | 10.1007/s10044-015-0496-9 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1007/s10044-015-0496-9 Verlag, Volltext: https://link.springer.com/article/10.1007/s10044-015-0496-9 
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| Author Notes: | Nikolaos Gianniotis, Christoph Schnörr, Christian Molkenthin, Sanjay Singh Bora |
| Summary: | Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lower bound is then optimised with respect to its free parameters, the so-called variational parameters. However, this is not always possible as for certain integrals it is very challenging (or tedious) to come up with a suitable lower bound. Here, we propose a simple scheme that overcomes some of the awkward cases where the usual variational treatment becomes difficult. The scheme relies on a rewriting of the lower bound on the model log-likelihood. We demonstrate the proposed scheme on a number of synthetic and real examples, as well as on a real geophysical model for which the standard variational approaches are inapplicable. |
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| Item Description: | Published online: 30 June 2015 Gesehen am 19.12.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1433-755X |
| DOI: | 10.1007/s10044-015-0496-9 |