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Empirical Inference Probabilistic Numerics Conference Paper 2012

Approximate Gaussian Integration using Expectation Propagation

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Probabilistic Numerics, Empirical Inference
Philipp Hennig
Affiliated Researcher

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
Bibtex Type: Conference Paper (inproceedings)
Event Name: -
State: Submitted
Digital: 0
Electronic Archiving: grant_archive
Links:

BibTex 

@inproceedings{CunninghamHL2012,
  title = {Approximate Gaussian Integration using Expectation Propagation},
  abstract = {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. },
  pages = {1-11},
  month = jan,
  year = {2012},
  slug = {cunninghamhl2012},
  author = {Cunningham, JP. and Hennig, P. and Lacoste-Julien, S.},
  month_numeric = {1}
}