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 language | English (US) |
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Pages (from-to) | 1-78 |
Number of pages | 78 |
Journal | Journal of Machine Learning Research |
Volume | 18 |
State | Published - Apr 1 2018 |
Funding
The authors are grateful for the support of NSF CAREER Award DMS1454377, NSF IIS1408910, NSF IIS1332109, NIH R01MH102339, NIH R01GM083084, and NIH R01HG06841. This work is also supported by an IBM Corporation Faculty Research Fund at the University of Chicago Booth School of Business. This work was completed in part with resources provided by the University of Chicago Research Computing Center.
Keywords
- Graphical model selection
- Hypothesis test
- Nonparanormal graph
- Regularized rank-based estimator
- Time-varying network analysis
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Statistics and Probability
- Artificial Intelligence