Loss-calibrated expectation propagation for approximate Bayesian decision-making

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Morais, Michael J, Pillow, Jonathan W
Format: Article
Language:English
Subjects:
Approximation
Asymmetry
Bayesian analysis
Calibration
Decision making
Expected utility
Gaussian process
Machine learning
Propagation
Statistical inference
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Summary:Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.
ISSN:2331-8422