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Approximate Gaussian Integration using Expectation Propagation

2012

Conference Paper

ei

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While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We offer here an empirical study of the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approximation is highly accurate. We also extend the derivations to the more general case of polyhedral integration regions. However, we find that in this polyhedral case, EP's answer, though often accurate, can be almost arbitrarily wrong. These unexpected results elucidate an interesting and non-obvious feature of EP not yet studied in detail, both for the problem of Gaussian probabilities and for EP more generally.

Author(s): Cunningham, JP. and Hennig, P. and Lacoste-Julien, S.
Pages: 1-11
Year: 2012
Month: January
Day: 0

Department(s): Empirical Inference, Probabilistic Numerics
Bibtex Type: Conference Paper (inproceedings)

Event Name: -

Digital: 0
State: Submitted

Links: Web

BibTex

@inproceedings{CunninghamHL2012,
  title = {Approximate Gaussian Integration using Expectation Propagation},
  author = {Cunningham, JP. and Hennig, P. and Lacoste-Julien, S.},
  pages = {1-11},
  month = jan,
  year = {2012},
  month_numeric = {1}
}