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April 2019 Combinatorial inference for graphical models
Matey Neykov, Junwei Lu, Han Liu
Ann. Statist. 47(2): 795-827 (April 2019). DOI: 10.1214/17-AOS1650

Abstract

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity, the presence of a cycle of certain size, or the maximum degree of the graph. To begin with, we study the information-theoretic limits of a large family of combinatorial inference problems. We propose new concepts including structural packing and buffer entropies to characterize how the complexity of combinatorial graph structures impacts the corresponding minimax lower bounds. On the other hand, we propose a family of novel and practical structural testing algorithms to match the lower bounds. We provide numerical results on both synthetic graphical models and brain networks to illustrate the usefulness of these proposed methods.

Citation

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Matey Neykov. Junwei Lu. Han Liu. "Combinatorial inference for graphical models." Ann. Statist. 47 (2) 795 - 827, April 2019. https://doi.org/10.1214/17-AOS1650

Information

Received: 1 August 2016; Revised: 1 August 2017; Published: April 2019
First available in Project Euclid: 11 January 2019

zbMATH: 07033152
MathSciNet: MR3909951
Digital Object Identifier: 10.1214/17-AOS1650

Subjects:
Primary: 62F03, 62F04, 62H15

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 2 • April 2019
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