A0722
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 various assumptions, often, for instance, in standard conformal prediction, relying on the invariance of the data distribution under special groups of transformations, such as permutation groups. SymmPI is proposed, a methodology for predictive inference when data distributions have general group symmetries in arbitrary observation models. 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 by distribution shift, recovering recent results as special cases. SymmPI is applied to predict unobserved values associated with vertices in a network, where the distribution is unchanged under relabeling that keep the network structure unchanged. In several simulations in a two-layer hierarchical model and in an empirical data analysis example, SymmPI performs favorably compared to existing methods.
