  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.

Machine Learning;Machine Learning