Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation

TL;DR

This paper introduces a neural network-based amortized inference method for generalized Bayesian posteriors that significantly reduces computational costs and enables rapid sampling across different datasets and temperature parameters.

Contribution

It presents the first fully amortized variational approximation for tempered posteriors, eliminating the need for repeated costly inference procedures for each dataset and temperature value.

Findings

Achieves competitive posterior approximations across multiple benchmarks.

Matches MCMC-based samplers in accuracy over various temperature settings.

Provides a scalable, single-pass sampling method without simulator calls.

Abstract

Generalized Bayesian Inference (GBI) tempers a loss with a temperature $\beta>0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers and must be re-run for each new dataset and each $\beta$ value. We give the first fully amortized variational approximation to the tempered posterior family $p_\beta(\theta \mid x) \propto \pi(\theta)\,p(x \mid \theta)^\beta$ by training a single $(x,\beta)$-conditioned neural posterior estimator $q_\phi(\theta \mid x,\beta)$ that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: (i) synthesize off-manifold samples $(\theta,x) \sim \pi(\theta)\,p(x \mid \theta)^\beta$ and (ii) reweight a fixed base dataset $\pi(\theta)\,p(x \mid \theta)$ using self-normalized importance sampling (SNIS). We show that the SNIS-weighted objective provides a consistent forward-KL fit to the tempered posterior with finite weight variance. Across four standard simulation-based inference (SBI) benchmarks, including the chaotic Lorenz-96 system, our $\beta$-amortized estimator achieves competitive posterior approximations in standard two-sample metrics, matching non-amortized MCMC-based power-posterior samplers over a wide range of temperatures.