Combinatorial inference for graphical models

Matey Neykov, Junwei Lu, Han Liu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)795-827
Number of pages33
JournalAnnals of Statistics
Issue number2
StatePublished - Apr 2019


  • Graph structural inference
  • Minimax testing
  • Multiple hypothesis testing
  • Post-regularization inference
  • Uncertainty assessment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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