Speaker: Dr. Jungeum Kim
Title: Tree Regression in Statistical Uncertainty Quantification for Generative AI
Abstract: This talk will explore statistical uncertainty quantification through tree regression modeling, focusing on three distinct aspects. First, we will discuss MCMC mixing rates for Bayesian tree models, highlighting conditions for efficient mixing and addressing the limitations of the standard grow-and-prune steps. We will introduce Twiggy Bayesian CART, a novel proposal mechanism that ensures faster convergence by exploring entire tree structures rather than individual nodes. Next, we will address posterior sampling with obscured likelihoods using Approximate Bayesian Computation (ABC). To improve efficiency, we propose a self-aware, tree-based framework that refines high-likelihood regions and accelerates sampling through a binary bandit approach. This method successfully applies to masked image recovery, demonstrating its effectiveness in uncertainty quantification for generative deep learning models. Finally, we will examine conformal prediction in contemporary applications, including generative AI. Using adaptive partitioning with a new robust regression tree algorithm, we develop a two-stage calibration framework for conformal prediction, enabling locally adaptive uncertainty quantification for black-box models like GPT-4. Applications include conformalized predictions for skin disease diagnoses based on self-reported symptoms.