无标定鲁棒贝叶斯推断用于离散非归一化模型
Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models
- Texas A&M University（得克萨斯农工大学）
- University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出DFD-BETEL，一种无需标定的半参数贝叶斯框架，通过离散Fisher散度矩条件实现非归一化离散模型的鲁棒推断，保证渐近校准的不确定性量化。
AI中文摘要：
对于具有难处理归一化常数的离散模型，贝叶斯推断在计算上具有挑战性，尤其是在样本空间较大或可数无限的情况下。尽管一些基于似然的贝叶斯方法可以规避难处理的归一化常数，但在模型误设定下，其不确定性量化可能校准不良。广义贝叶斯方法可以解决这一校准问题，但通常需要仔细调整学习率。在本文中，我们提出DFD-BETEL，一种半参数贝叶斯框架，利用离散Fisher散度的一阶最优性条件作为贝叶斯指数倾斜经验似然中的矩条件。由此得到的后验避免了归一化常数的计算，且无需学习率校准。我们建立了离散Fisher散度估计量的一致性和渐近正态性，并证明了DFD-BETEL后验的Bernstein-von Mises定理，表明其极限协方差与估计量的抽样协方差相匹配，从而产生渐近校准的不确定性量化。数值研究表明，在正确设定下，DFD-BETEL与基于似然的贝叶斯推断保持竞争力，并在模型误设定下提供更可靠的不确定性量化。对汽车保险索赔数据的应用进一步说明了DFD-BETEL的实际效用。
英文摘要：
Bayesian inference for discrete models with intractable normalizing constants is computationally challenging, particularly when the sample space is large or countably infinite. Although some likelihood-based Bayesian methods can circumvent the intractable normalizing constant, their uncertainty quantification may be poorly calibrated under model misspecification. Generalized Bayesian approaches can address this calibration issue, but typically require careful tuning of a learning rate. In this paper, we propose DFD-BETEL, a semiparametric Bayesian framework that uses the first-order optimality conditions of discrete Fisher divergence as moment conditions in Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of the normalizing constant and requires no learning-rate calibration. We establish consistency and asymptotic normality of the discrete Fisher divergence estimator and prove a Bernstein-von Mises theorem for the DFD-BETEL posterior, showing that its limiting covariance matches the sampling covariance of the estimator and yields asymptotically calibrated uncertainty quantification. Numerical studies show that DFD-BETEL remains competitive with likelihood-based Bayesian inference under correct specification and provides more reliable uncertainty quantification under model misspecification. An application to automobile-insurance claim data further illustrates the practical utility of DFD-BETEL.
