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

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.

💡 Research Summary

This paper tackles the computational bottleneck of generalized Bayesian inference (GBI) in simulation‑based inference (SBI) settings by introducing a fully amortized variational approximation to the whole family of tempered posteriors
(p_{\beta}(\theta\mid x)\propto\pi(\theta),p(x\mid\theta)^{\beta}).
Instead of running a costly MCMC or stochastic‑differential‑equation sampler for each new observation and each temperature β, the authors train a single neural posterior estimator (q_{\phi}(\theta\mid x,\beta)) that is conditioned on both the data x and the temperature β. Once trained, sampling from any desired power‑posterior requires only one forward pass through the network—no simulator calls, no iterative inference.

Two complementary training routes are proposed.

Route A (Score‑assisted tempered synthesis).
First, a joint score network (s_{\psi}(\theta,x)=\nabla_{\theta,x}\log\bigl