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Annual Review of Statistics and Its Application

Volume 12, 2025

Neural Methods for Amortized Inference

  • Andrew Zammit-Mangion1, Matthew Sainsbury-Dale1,2 and Raphaël Huser2
  • 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; email: [email protected] 2Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
  • Vol. 12:311-335 (Volume publication date March 2025)
  • First published as a Review in Advance on November 12, 2024
  • Copyright © 2025 by the author(s).
    This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information.

Abstract

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries, and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

Keyword(s): approximate Bayesian inference, likelihood approximation, likelihood-free inference, neural networks, simulation-based inference, variational Bayes
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2025-03-07
2025-06-19
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Neural Methods for Amortized Inference
Annual Review of Statistics and Its Application 12, 311 (2025); https://doi.org/10.1146/annurev-statistics-112723-034123
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