# Loss-calibrated expectation propagation for approximate Bayesian decision-making

arXiv: https://arxiv.org/abs/2201.03128 · HTML: https://mlsanity.com/paper/2201.03128/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 10 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Loss-Calibrated Approximate Inference in Bayesian Neural Networks](https://mlsanity.com/paper/1805.03901/) (2018)
- [Variational Bayesian Decision-making for Continuous Utilities](https://mlsanity.com/paper/1902.00792/) (2019)
- [Direct loss minimization algorithms for sparse Gaussian processes](https://mlsanity.com/paper/2004.03083/) (2020)
- [Correcting Predictions for Approximate Bayesian Inference](https://mlsanity.com/paper/1909.04919/) (2019)

## Built on by (most cited first, 5 of 5)

- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Approximation-Aware Bayesian Optimization](https://mlsanity.com/paper/2406.04308/) (2024)
- [Long-tailed Classification from a Bayesian-decision-theory Perspective](https://mlsanity.com/paper/2303.06075/) (2023)
- [Understanding and mitigating difficulties in posterior predictive evaluation](https://mlsanity.com/paper/2405.19747/) (2024)
- [Making Reliable and Flexible Decisions in Long-tailed Classification](https://mlsanity.com/paper/2501.14090/) (2025)

## Abstract (arXiv)

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.