Abstract

Reproducible learning of the underlying structure among large-scale

network data is important in many contemporary applications. Despite the fastgrowing literature on this subject, the practical issue of data heterogeneity has

rarely been addressed. In this paper, we propose a new method called the multiple graphical knockofffilter to efficiently recover the underlying sparse connected

structure of a general population from a high-dimensional heterogeneous dataset.

We provide theoretical justification on the asymptotic false discovery rate control, and the theory for the power analysis is also established. To the best of

our knowledge, this is the first formal theoretical result on the power for the

graphical knockoffs procedure. Our new methodology and results are evidenced

by numerical studies.

Information

Preprint No.SS-2023-0099
Manuscript IDSS-2023-0099
Complete AuthorsJia Zhou, Guangming Pan, Zeming Zheng, Changchun Tan
Corresponding AuthorsJia Zhou
Emailstszhjia@mail.ustc.edu.cn

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Acknowledgments

We thank the editor, associate editor, and referees for their insightful comments. Zheng’s research is supported by the National Key Research and De-

velopment Program of China (Grant No. 2022YFA1008000). Pan’s research

is supported by the Ministry of Education, Singapore (Grant No. MOE-

Zhou’s research is supported by the Natural Science

Foundation of Hefei University of Technology (Grant No. JZ2023HGQA0085).

Supplementary Materials

available online include four auxiliary lemmas,

the proofs for all lemmas and Theorems 1-2, and two figures of real data

analysis mentioned in Section 5.

Supplementary materials are available for download.