Structured Conformal Inference for Matrix Completion with Applications to Group Recommender Systems

• 成果类型: Article; Early Access
• 署名作者: Liang, Ziyi; Xie, Tianmin; Tong, Xin; Sesia, Matteo
• 署名单位: University of California System; University of California Irvine; University of Southern California; University of Hong Kong; University of Southern California
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2658287
• 发表日期: 2026-06-06
• 关键词: Collaborative filtering; Uncertainty-aware group recommendations; confidence regions; conformal inference; Simultaneous Inference; uncertainty estimation

摘要

We develop a conformal inference method to construct joint prediction regions for structured groups of missing entries in a sparsely observed matrix, focusing on groups drawn from the same column. The method can be combined with any black-box matrix completion algorithm and makes no distributional assumptions for the underlying data matrix; instead, it obtains rigorous inferences by modeling the missingness mechanism. In the context of recommender systems, for example, it is useful to quantify uncertainty in the ratings that all members of a group would assign to the same item, enabling more informed decisions when individual preferences may conflict. Unlike existing conformal techniques that estimate uncertainty for one entry at a time, our approach provides group-level guarantees by assembling calibration data with matching structure. To achieve this, we introduce a generalized weighted conformalization framework that addresses the lack of exchangeability induced by structured calibration, along with computational strategies that make the method practical at scale. We demonstrate the effectiveness of our approach through synthetic experiments under various missing-data mechanisms and applications to MovieLens datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.