  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.
