Neural Methods for Amortized Inference
This is an incremental review paper summarizing existing advancements in neural methods for amortized inference, aimed at researchers in statistics and machine learning.
The article reviews recent progress in using neural networks and computational tools for amortized inference, which enables rapid statistical inference after an initial setup, highlighting benefits over traditional methods like Markov chain Monte Carlo.
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.