Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation
This work addresses the problem of slow inference in GBI for researchers and practitioners, offering a more efficient method, though it is incremental as it builds on existing neural posterior estimation techniques.
The paper tackles the computational inefficiency of Generalized Bayesian Inference (GBI) by proposing the first fully amortized variational approximation to tempered posteriors, enabling sampling in a single forward pass without costly MCMC or simulator calls. It achieves competitive posterior approximations across four SBI benchmarks, matching non-amortized MCMC-based methods over a wide temperature range.
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.