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. 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.
Author details: | Nikolaos Gianniotis, Christoph Schnoerr, Christian MolkenthinGND, Sanjay Singh BoraGND |
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DOI: | https://doi.org/10.1007/s10044-015-0496-9 |
ISSN: | 1433-7541 |
ISSN: | 1433-755X |
Title of parent work (English): | Pattern Analysis & Applications |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Tag: | Bayesian inference; Expectation maximisation; Posterior estimation |
Volume: | 19 |
Number of pages: | 11 |
First page: | 475 |
Last Page: | 485 |
Funding institution: | BMBF; graduate research school GeoSim of the Geo.X initiative |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Geowissenschaften |
Peer review: | Referiert |
Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Erd- und Umweltwissenschaften |