Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted empirical likelihood carefully designed to concentrate near a parametric family of distributions of choice with respect to a novel variant of the Wasserstein metric, which is then combined with a prior distribution on model parameters to obtain a robustified posterior. The proposed approach finds applications in a wide variety of robust inference problems, where we intend to perform inference on the parameters associated with the centering distribution in presence of outliers. Our proposed transport metric enjoys great computational simplicity, exploiting the Sinkhorn regularization for discrete optimal transport problems, and being inherently parallelizable. We demonstrate superior performance of our methodology when compared against state-of-the-art robust Bayesian inference methods. We also demonstrate equivalence of our approach with a nonparametric Bayesian formulation under a suitable asymptotic framework, testifying to its flexibility. The constrained entropy maximization that sits at the heart of our likelihood formulation finds its utility beyond robust Bayesian inference; an illustration is provided in a trustworthy machine learning application.

翻译：灵活贝叶斯模型通常通过包含大量不可解释参数的大规模参数模型极限来构建。本文提出一种全新替代方案：构造指数倾斜的经验似然函数，该函数通过新型Wasserstein度量变体，被精心设计为在选定的参数化分布族附近集中分布，随后与模型参数先验分布结合以生成稳健化后验。所提方法适用于多种稳健推断问题——当数据存在异常值时，我们仍试图推断中心化分布的相关参数。本文提出的输运度量具有显著计算简便性，不仅利用Sinkhorn正则化处理离散最优输运问题，且天然具备可并行化特性。与最先进的稳健贝叶斯推断方法相比，本文方法展现出更优性能。同时，我们在合适的渐近框架下证明了该方法与非参数贝叶斯公式的等价性，验证了其灵活性。这种构成似然函数核心的约束熵最大化方法，其应用价值远超稳健贝叶斯推断范畴——我们通过可信机器学习应用实例进行了佐证。