A0190
Title: Distribution-free matrix prediction under arbitrary missing pattern
Authors: Yuan Zhang - The Ohio State University (United States) [presenting]
Meijia Shao - The Ohio State University (United States)
Abstract: The purpose is to study the open problem of conformalized entry prediction in a row/column-exchangeable matrix. The matrix setting presents novel and unique challenges, but there exists little work on this interesting topic. The problem is meticulously defined, differentiating it from closely related problems and rigorously delineating the boundary between achievable and impossible goals. Two practical algorithms are then proposed. The first method provides a fast emulation of the full conformal prediction, while the second method leverages the technique of algorithmic stability for acceleration. Both methods are computationally efficient and can effectively safeguard coverage validity in the presence of arbitrary missing patterns. Further, the impact of missingness on prediction accuracy is quantified and fundamental limit results are established. Empirical evidence from synthetic and real-world datasets corroborates the superior performance of the proposed methods.
