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

TL;DR

This work tackles robust simulation-based inference under model misspecification by embedding Generalized Bayesian Inference into a fully amortized neural posterior estimator conditioned on data and tempering, $q_φ(θ\mid x,β)$. It introduces two training routes: Route A, which uses score-guided tempered synthesis to generate training triples and distill $p_β(θ\mid x)$ into a single conditioner, and Route B, which reweights a fixed base joint via self-normalized importance sampling to learn the same conditional. Across four SBI benchmarks and a Hodgkin--Huxley model, the amortized estimator closely tracks ground-truth power posteriors with no test-time simulator queries or MCMC, offering a scalable and robust alternative for temperature-varying inference. The approach balances robustness (Route A) and efficiency (Route B) and provides finite-variance SNIS guarantees for certain tempering regimes, enabling practical deployment for sensitivity analyses and robustness studies.

Abstract

Generalized Bayesian Inference (GBI) tempers a loss with a temperature $β>0$ 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 $β$ value. We give the first fully amortized variational approximation to the tempered posterior family $p_β(θ\mid x) \propto π(θ)\,p(x \mid θ)^β$ by training a single $(x,β)$-conditioned neural posterior estimator $q_φ(θ\mid x,β)$ 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 $(θ,x) \sim π(θ)\,p(x \mid θ)^β$ and (ii) reweight a fixed base dataset $π(θ)\,p(x \mid θ)$ 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 $β$-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.

Figures (5)

• Figure 1: Route A/B comparison across benchmarks with a shared legend.
• Figure 2: HH parameter marginals under RouteB_NLE for $\beta\in\{0.1,1.0,2.0\}$ (10K simulations).
• Figure 3: Three observations from the Allen Cell Types Database and RouteB-NLE predictive samples.
• Figure 4: Gaussian mixture. Qualitative effect of the power posterior across different $\beta$ values. Rows correspond to $\beta \in \{0.1, 0.7, 1.5\}$ and columns show samples from the reference power posterior (left), Route A (middle), and Route B (NRE-SNIS; right).
• Figure 5: Two moons. Qualitative effect of the power posterior across different $\beta$ values. Rows correspond to $\beta \in \{0.1, 0.7, 1.5\}$ and columns show samples from the reference power posterior (left), Route A (middle), and Route B (NRE-SNIS; right).

Theorems & Definitions (8)

• Proposition 4.1
• Proposition 4.2
• Lemma 2.1
• proof
• proof
• proof
• Proposition 2.2
• proof