Local and Global Inference for High Dimensional Nonparanormal Graphical Models

TL;DR

This paper introduces a unified, tuning-parameter-free inferential framework for high-dimensional nonparanormal graphical models, enabling testing of individual edges and confidence subgraph construction without Gaussian assumptions.

Contribution

It develops a novel pseudo likelihood approach and a bootstrap method for inference that extends existing frameworks and handles unknown marginal transformations.

Findings

Method accurately tests edge presence in high dimensions.

Constructs confidence subgraphs with high probability coverage.

Does not rely on Gaussian or sub-Gaussian assumptions.

Abstract

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach. In sharp contrast to the existing high dimensional score test method, our method is free of tuning parameters given an initial estimator, and extends the scope of the existing likelihood based inferential framework. Furthermore, we propose a U-statistic multiplier bootstrap method to construct the confidence subgraph. We show that the constructed subgraph is contained in the true graph with probability greater than a given nominal level. Compared with existing methods for constructing confidence subgraphs, our method does not rely on Gaussian or sub-Gaussian assumptions. The theoretical properties of the proposed inferential methods are verified by thorough numerical experiments and real data analysis.