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Empirical Inference Probabilistic Numerics Technical Report 2009

Expectation Propagation on the Maximum of Correlated Normal Variables

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Probabilistic Numerics, Empirical Inference
Philipp Hennig
Affiliated Researcher

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

Author(s): Hennig, P.
Links:
Year: 2009
Month: July
Day: 0
Bibtex Type: Technical Report (techreport)
Digital: 0
Electronic Archiving: grant_archive
Institution: Cavendish Laboratory: University of Cambridge

BibTex 

@techreport{Hennig2009,
  title = {Expectation Propagation on the Maximum of Correlated Normal Variables},
  abstract = {Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities. },
  institution = {Cavendish Laboratory: University of Cambridge},
  month = jul,
  year = {2009},
  slug = {hennig2009},
  author = {Hennig, P.},
  month_numeric = {7}
}