基于约束传输度量的鲁棒概率推理
Robust probabilistic inference via a constrained transport metric
摘要：
灵活的贝叶斯模型通常是使用具有许多通常无法解释的参数的大型参数模型的限制来构建的。在这篇文章中，我们提供了一种新的替代方法，通过构建一个指数倾斜的经验似然精心设计，集中在一个参数家庭的选择相对于一个新的变量的Wasserstein度量，然后结合模型参数的先验分布，以获得鲁棒后验分布。所提出的方法在各种各样的鲁棒推理问题中找到了应用，在这些问题中，我们打算在存在离群值的情况下对与中心分布相关的参数进行推理。我们提出的运输度量具有很大的计算简单性，利用Sinkhorn正则化离散最优运输问题，并具有内在的并行化。我们展示了优越的性能，我们的方法相比，国家的最先进的强大的贝叶斯推断方法。我们还证明了我们的方法与一个合适的渐近框架下的非参数贝叶斯公式的等价性，证明了它的灵活性。约束熵最大化，坐在我们的似然公式的心脏，发现其效用超出强大的贝叶斯推断;一个值得信赖的机器学习应用程序中提供的说明。
英文摘要：
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.
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