Post-Regularization Inference for Time-Varying Nonparanormal Graphical Models
This work addresses the challenge of inferring dynamic network structures in high-dimensional, heavy-tailed data for fields like neuroscience, representing an incremental advancement by extending nonparanormal models to time-varying settings.
The authors tackled the problem of modeling high-dimensional heavy-tailed systems with evolving network structures by proposing time-varying nonparanormal graphical models, developing statistical tests for edge presence that are robust to model selection and do not require minimum signal strength, with results including minimax optimal convergence rates and validation through simulations and neural imaging data.
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.