# Approximate inference for the loss-calibrated Bayesian

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Simon Lacoste–Julien,
Ferenc Huszár,
Zoubin Ghahramani
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Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:416-424, 2011.

#### Abstract

We consider the problem of approximate inference in the context of Bayesian decision theory. Traditional approaches focus on approximating general properties of the posterior, ignoring the decision task – and associated losses – for which the posterior could be used. We argue that this can be suboptimal and propose instead to loss-calibrate the approximate inference methods with respect to the decision task at hand. We present a general framework rooted in Bayesian decision theory to analyze approximate inference from the perspective of losses, opening up several research directions. As a first loss-calibrated approximate inference attempt, we propose an EM-like algorithm on the Bayesian posterior risk and show how it can improve a standard approach to Gaussian process classification when losses are asymmetric.

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