博士生讨论班2025[23]
时间：2025-11-10
阅读量：167次
- 演讲人： 赵冠岚
- 时间：2025年11月11日14:00
- 地点：浙江大学紫金港校区行政楼1417报告厅
- 主办单位：浙江大学数据科学研究中心
报告文章：SymmPI: Predictive Inference for Data with Group Symmetries（Edgar Dobriban and Mengxin Yu∗）
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 to vertices in a network, where the distribution is unchanged under relabelings 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.