通过神经后验估计在广义贝叶斯中进行摊销的基于模拟的推理
Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation
AI总结：
提出一种通过训练单一数据与β条件神经后验估计器来摊销广义贝叶斯推理中温度参数β的方法，无需模拟器调用或推理时MCMC，实现单次前向传播采样。
摘要：
广义贝叶斯推理（GBI）通过温度β>0调整损失以减轻过度自信并提高模型误设下的鲁棒性，但现有GBI方法通常依赖昂贵的MCMC或基于SDE的采样器，且必须为每个新数据集和每个β值重新运行。我们通过训练单一数据与β条件神经后验估计器，首次为温度后验族提供了完全摊销的变分近似，使得单次前向传播即可采样，无需模拟器调用或推理时MCMC。我们引入了两种互补的训练路径：一种从温度联合分布中合成流形外样本，另一种使用自归一化重要性采样（SNIS）对固定基础数据集进行重加权。我们证明，SNIS加权目标在有限权重方差下为温度后验提供了一致的前向KL拟合。在四个标准基于模拟的推理基准（包括混沌Lorenz-96系统）中，我们的β摊销估计器在标准双样本指标上实现了具有竞争力的后验近似，在广泛温度范围内匹配了非摊销的基于MCMC的幂后验采样器。
英文摘要：
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 for the tempered posterior family by training a single data- and $β$-conditioned neural posterior estimator that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: one synthesizes off-manifold samples from the tempered joint distribution, and the other reweights a fixed base dataset 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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
