|
Abstract:
|
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often un-interpretable. In this article, we offer a novel get-around by proposing an exponentially tilted empirical likelihood carefully designed to concentrate near a simpler parametric family of distributions of choice with respect to a modified Wasserstein metric. It finds applications in a wide variety of robust inference problems, where we intend to make inference on the parameters associated with the centering distribution in presence of outliers. Importantly, our novel formulation of the modified Wasserstein metric enjoys great computational simplicity, exploiting the Sinkhorn regularization of discrete optimal transport problem, and inherently parallelizable. We demonstrate superior performance of this technology when compared against some of the state-of-the-art robust Bayesian inference methods. Moreover, the constrained entropy maximization setup that sits at the heart of our likelihood formulation, finds its utility beyond robust Bayesian inference; particularly in the fields of entropy-based portfolio allocation and group fairness.
|
