Post-regularization inference for time-varying nonparanormal graphical models

Junwei Lu, Mladen Kolar, Han Liu

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both the index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Our method is supported by thorough numerical simulations and an application to a neural imaging data set.

Original languageEnglish (US)
Pages (from-to)1-78
Number of pages78
JournalJournal of Machine Learning Research
Volume18
StatePublished - Apr 1 2018

Keywords

  • Graphical model selection
  • Hypothesis test
  • Nonparanormal graph
  • Regularized rank-based estimator
  • Time-varying network analysis

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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