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Post-regularization inference for time-varying nonparanormal graphical models

Author(s): Lu, J; Kolar, M; Liu, H

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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.
Publication Date: 2018
Citation: Lu, Junwei, Mladen Kolar, and Han Liu. "Post-regularization inference for time-varying nonparanormal graphical models." The Journal of Machine Learning Research, 18 (2017): 1-78.
ISSN: 1532-4435
EISSN: 1533-7928
Pages: 1 - 78
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Machine Learning Research
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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