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

arXiv:2601.22367v1 Announce Type: new
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.