JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models

TL;DR

JANA introduces a novel neural approach to jointly approximate likelihoods and posteriors in Bayesian inference, enabling efficient and scalable simulation-based analysis with improved calibration and applicability to complex time series.

Contribution

The paper presents a new end-to-end neural framework that jointly amortizes likelihoods and posteriors, enhancing Bayesian inference for complex models.

Findings

JANA achieves high fidelity in approximating Bayesian models.

It provides a diagnostic tool for calibration.

Recurrent likelihood networks can emulate complex time series models.

Abstract

This work proposes ``jointly amortized neural approximation'' (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation -- two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state-of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.