Weighted Bayesian Bootstrap for Scalable Bayes

TL;DR

The paper introduces Weighted Bayesian Bootstrap (WBB), a scalable and fast method for uncertainty quantification in complex models, leveraging existing optimization tools like TensorFlow.

Contribution

It presents WBB as a novel, computationally efficient approach for Bayesian uncertainty quantification applicable to diverse machine learning models.

Findings

WBB provides accurate uncertainty estimates in regularized regression.

WBB is scalable and compatible with off-the-shelf optimization software.

Demonstrated effectiveness in deep learning and trend filtering.

Abstract

We develop a weighted Bayesian Bootstrap (WBB) for machine learning and statistics. WBB provides uncertainty quantification by sampling from a high dimensional posterior distribution. WBB is computationally fast and scalable using only off-theshelf optimization software such as TensorFlow. We provide regularity conditions which apply to a wide range of machine learning and statistical models. We illustrate our methodology in regularized regression, trend filtering and deep learning. Finally, we conclude with directions for future research.