Weighted Bayesian Bootstrap for Scalable Bayes

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.