This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions.

We propose a general framework to design posterior sampling methods for model-based RL. We show that the proposed algorithms can be analyzed by reducing regret to Hellinger distance in conditional probability estimation. We further show that optimistic posterior sampling can control this Hellinger distance, when we measure model error via data likelihood. This technique allows us to design and analyze unified posterior sampling algorithms with state-of-the-art sample complexity guarantees for many model-based RL settings. We illustrate our general result in many special cases, demonstrating the versatility of our framework.

QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas.

Unfortunately, Sparse VI and PSVI rely on access to exact samples from the model posterior and closed form gradients of it to be evaluated and updated.

Submitted by Assigned_Reviewer_1 Q1 The authors design and fit a hierarchical Bayesian model for predicting disease trajectories (i.e., a scalar measure of disease severity measured throughout the course of the disease) for individual patients. The overall model is an additive combination of a a number of terms including: (1) a population-level term, (2) a subpopulation term, (3) an individual term, (4) a GP term for structured errors. Each of these terms is a function of time, which is modeled parametrically in terms of the coefficients on pre-defined basis expansions (linear and/or B-splines). The subpopulation term involves a discrete mixture model, and the individual level term is a Bayesian linear regression. Distributions are chosen to be Gaussian, which makes most steps of inference and learning work out nicely.