Expectation Propagation on the Maximum of Correlated Normal Variables

2009/10/01 by Philipp Hennig, Hennig, Philipp
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Neural Networks and Applications #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.0910.0115

openalex publication_date 2009/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Inverse Optimization

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