A0608
Title: SymmPI: Predictive inference for data with group symmetries
Authors: Mengxin Yu - Washington University in St. Louis (United States) [presenting]
Abstract: Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often, for instance, in standard conformal prediction, relying on the invariance of the distribution of the data under special groups of transformations such as permutation groups. Moreover, many existing methods for predictive inference aim to predict unobserved outcomes in sequences of feature-outcome observations. Meanwhile, there is interest in predictive inference under more general observation models (e.g., for partially observed features) and for data satisfying more general distributional symmetries (e.g., network, rotationally invariant, or coordinate-independent observations in physics). SymmPI is proposed, a unified methodology for predictive inference when data distributions have general group symmetries in arbitrary observation models. The methods leverage the novel notion of distributional equivariant transformations, which process the data while preserving their distributional invariances. It is shown that SymmPI has valid coverage under distributional invariance, and its performance is characterized under distribution shift, recovering recent results as special cases. These methodologies are particularly relevant for cluster-randomized trials in clinical settings, where prediction reliability is essential.
