SymmPI: predictive inference for data with group symmetries

• 成果类型: Article; Early Access
• 署名作者: Dobriban, Edgar; Yu, Mengxin
• 署名单位: University of Pennsylvania; Washington University (WUSTL)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf022
• 发表日期: 2025
• 关键词: permutation; tests; validity

摘要

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. rotationally invariant observations in physics). Here, we propose SymmPI, a methodology for predictive inference when data distributions have general group symmetries in arbitrary observation models. Our methods leverage the novel notion of distributionally equivariant transformations, which process the data while preserving their distributional invariances. We show that SymmPI has valid coverage under distributional invariance and characterize its performance under distribution shift, recovering recent results as special cases. We apply SymmPI to predict unobserved values associated with vertices in a network, where the distribution is unchanged under relabellings that keep the network structure unchanged. In several simulations in a two-layer hierarchical model, and in an empirical data analysis example, SymmPI performs favourably compared with existing methods.