Learning the distance for ABC and localized neural posterior estimation

2026-06-22

AI Summary

This work addresses the challenge of Bayesian inference in misspecified time series models when the likelihood function is intractable but data can be simulated. It proposes an adaptive distance learning approach grounded in scoring rule optimization, which unifies the frameworks of Approximate Bayesian Computation (ABC) and localized Neural Posterior Estimation with Predictive Function Networks (NPE-PFN). The method establishes a theoretical equivalence between adaptive distance learning and the estimation of optimal linear combination weights for predictors. Empirical evaluations on both synthetic and real-world datasets demonstrate that the proposed approach substantially improves posterior estimation accuracy and predictive performance, offering a novel and effective strategy for inference under model misspecification in dynamic settings.

Abstract

Likelihood-free inference methods can perform Bayesian inference when evaluating the likelihood is impractical but simulating synthetic data from the model is feasible. Approximate Bayesian computation (ABC) is a well-established likelihood-free approach that constructs particle posterior approximations by evaluating the similarity between simulated and observed data using a distance function, which is used in rejection or weighting steps. Here we extend previous work on adaptive distance learning for ABC to misspecified time series, while also exploring applications in neural posterior estimation using prior-data fitted networks (NPE-PFN) with localization. The adaptation of the distance that we consider optimizes out-of-sample predictive performance using a scoring rule. We also establish a connection between linear pooling for forecast combination and our posterior estimation methods with randomized distances, showing that empirical estimation of pooling weights can be interpreted as another form of adaptive distance learning. For both ABC algorithms and NPE-PFN methods with localization, adaptive distance learning improves forecasting performance in simulated and real examples.

Problem

• likelihood-free inference
• approximate Bayesian computation
• adaptive distance learning
• neural posterior estimation
• time series

Innovation

• adaptive distance learning
• approximate Bayesian computation
• neural posterior estimation
• localization
• scoring rules