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

Ziyi Liang, Tianmin Xie, Xin Tong, Matteo Sesia

Abstract: 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.