Generative Bayesian Inference

University Of Chicago, Chicago IL

Investigators

Abstract

As artificial intelligence (AI) continues to proliferate rapidly through society, there is a growing interest in incorporating core statistical principles, such as uncertainty quantification, into predictive systems to enable reliable and trustworthy AI decision-making. This research program aims to bridge the current conceptual gap between statistics and AI by ensuring that machine-assisted predictions are statistically valid, thereby supporting their safe and effective application to complex scientific challenges in data-rich domains such as imaging, personalized medicine, business analytics, marketing, and economics. The research agenda is organized around two overarching objectives, unified by a common thread: generative models in which data are viewed as stochastic outputs of computer programs. Conducting predictive inference in these models poses significant challenges due to their inherently opaque, black-box structure. The first objective is to develop a novel Bayesian inferential framework for generative models, leveraging modern machine learning tools such as deep learning and Bayesian Additive Regression Trees (BART). This work will lay the methodological and theoretical foundations for a new class of “generative Bayes” techniques that enable statistically principled inference in complex generative systems. The second objective focuses on advancing practical methodology for computerized adaptive testing (CAT), aimed at enhancing computer-human interactions through dynamically tailored questioning that adapts in real time to the respondent’s skill level with applications. The overarching goal of this research is to integrate modern machine learning tools into statistical modeling while establishing rigorous theoretical foundations that justify their practical use. The first project will develop a novel generative Bayesian framework for quantile-based learning using Bayesian Additive Regression Trees (BART). The outcome will be a flexible generative toolkit capable of simulating from a wide range of conditional distributions–core components for addressing numerous inferential tasks, including prediction. This work will chart a new path for nonparametric modeling of conditional distributions (such as posterior and posterior predictive distributions) via quantile learning under minimal assumptions. The methodological advances will be supported by a comprehensive frequentist-Bayesian theoretical analysis to assess the fidelity of distributional reconstructions. The second project will provide new theoretical insights into widely used sparsity-inducing priors, such as the horseshoe prior, by evaluating their performance from a predictive perspective. These contributions will deepen our understanding of the predictive properties of sparse Bayesian models and further enhance their applicability. The third project aims to bring machine learning techniques, particularly Q-learning, into the realm of computerized adaptive testing, thereby extending classical item response theory models to enable more responsive and individualized assessment tools. Together, these three projects will significantly advance the frontiers of nonparametric Bayesian methodology, theory, and applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.