Sean O'Hagan

Jungeum Kim, Sean O'Hagan, Veronika Rockova

This work is concerned with conformal prediction in contemporary applications (including generative AI) where a black-box model has been trained on data that are not accessible to the user. Mirroring split-conformal inference, we design a wrapper around a black-box algorithm which calibrates conformity scores. This calibration is local and proceeds in two stages by first adaptively partitioning the predictor space into groups and then calibrating sectionally group by group. Adaptive partitioning (self-grouping) is achieved by fitting a robust regression tree to the conformity scores on the calibration set. This new tree variant is designed in such a way that adding a single new observation does not change the tree fit with overwhelmingly large probability. This add-one-in robustness property allows us to conclude a finite sample group-conditional coverage guarantee, a refinement of the marginal guarantee. In addition, unlike traditional split-conformal inference, adaptive splitting and within-group calibration yields adaptive bands which can stretch and shrink locally. We demonstrate benefits of local tightening on several simulated as well as real examples using non-parametric regression. Finally, we consider two contemporary classification applications for obtaining uncertainty quantification around GPT-4o predictions. We conformalize skin disease diagnoses based on self-reported symptoms as well as predicted states of U.S. legislators based on summaries of their ideology. We demonstrate substantial local tightening of the uncertainty sets while attaining similar marginal coverage.

Sean O'Hagan, Veronika Ročková

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable information that can be integrated into a decision pipeline. Rather than seeing the lack of certitude and inherent randomness of GAI as a problem, we view it as an opportunity. Indeed, variable answers to given prompts can be leveraged to construct a prior distribution which reflects assuredness of AI predictions. This prior distribution may be combined with tailored datasets for a fully Bayesian analysis with an AI-driven prior. In this paper, we explore such a possibility within a non-parametric Bayesian framework. The basic idea consists of assigning a Dirichlet process prior distribution on the data-generating distribution with AI generative model as its baseline. Hyper-parameters of the prior can be tuned out-of-sample to assess the informativeness of the AI prior. Posterior simulation is achieved by computing a suitably randomized functional on an augmented data that consists of observed (labeled) data as well as fake data whose labels have been imputed using AI. This strategy can be parallelized and rapidly produces iid samples from the posterior by optimization as opposed to sampling from conditionals. Our method enables (predictive) inference and uncertainty quantification leveraging AI predictions in a coherent probabilistic manner.

Sean O'Hagan, Jungeum Kim, Veronika Rockova

In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance test. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past trials and errors. We apply recursive partitioning classifiers on the ABC lookup table to sequentially refine high-likelihood regions into boxes. Each box is regarded as an arm in a binary bandit problem treating ABC acceptance as a reward. Each arm has a proclivity for being chosen for the next ABC evaluation, depending on the prior distribution and past rejections. The method places more splits in those areas where the likelihood resides, shying away from low-probability regions destined for ABC rejections. We provide two versions: (1) ABC-Tree for posterior sampling, and (2) ABC-MAP for maximum a posteriori estimation. We demonstrate accurate ABC approximability at much lower simulation cost. We justify the use of our tree-based bandit algorithms with nearly optimal regret bounds. Finally, we successfully apply our approach to the problem of masked image classification using deep generative models.