Abstract

Incorporating auxiliary information alongside primary data can significantly

enhance the accuracy of simultaneous inference. However, existing multiple

testing methods face challenges in efficiently incorporating complex side information, especially when it differs in dimension or structure from the pri-

mary data, such as network side information. This paper introduces a locally

adaptive structure learning algorithm (LASLA), a flexible framework designed

to integrate a broad range of auxiliary information into the inference process. Although LASLA is specifically motivated by the challenges posed by

network-structured data, it also proves highly effective with other types of

side information, such as spatial locations and multiple auxiliary sequences.

LASLA employs a p-value weighting approach, leveraging structural insights

to derive data-driven weights that prioritize the importance of different hypotheses. Our theoretical analysis demonstrates that LASLA asymptotically

controls the false discovery rate (FDR) under independent or weakly dependent p-values, and achieves enhanced power in scenarios where the auxiliary

data provides valuable side information. Simulation studies are conducted to

evaluate LASLA’s numerical performance, and its efficacy is further illustrated

through two real-world applications.

Information

Preprint No.SS-2024-0002
Manuscript IDSS-2024-0002
Complete AuthorsZiyi Liang, T. Tony Cai, Wenguang Sun, Yin Xia
Corresponding AuthorsYin Xia
Emailsxiayin@fudan.edu.cn

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Acknowledgments

The research of Yin Xia was supported in part by the National Natural Science

Foundation of China (Grant No. 12331009). The research of Tony Cai was supported

in part by the National Science Foundation (Grant DMS-2413106) and the National

Institutes of Health (Grants R01-GM129781 and R01-GM123056).

Supplementary Materials

The Supplementary material includes numerical implementation details, additional

simulations and applications of LASLA, as well as theoretical results for the dependent case and the proofs of all theories.

Supplementary materials are available for download.