Nicholas Polson: Generative Bayes, E-values and Conformal Prediction

Generative Bayes, E-values and Conformal Prediction

Generative Bayesian Computation (GBC) methods are introduced. Prediction is a fundamental task in machine learning and modern-day statistics. There are a number of popular approaches: conformal prediction, fiducial prediction, marginal likelihood and full Bayes. E-values are used in testing problems. We provide a new look on Bayes testing and prediction. GBC methods directly modeling the predictive quantile map as a deep learner which leads to a number of theoretical and practical advantages over density-based methods. We illustrate our methodology in a number of examples, including sequential clinical trials and gaussian processes. Finally we conclude with directions for future research.