On Semiparametric Exponential Family Graphical Models

TL;DR

This paper introduces a flexible semiparametric exponential family graphical model for high-dimensional mixed data, allowing for unspecified base measures and providing new inference tools like a symmetric pairwise score test.

Contribution

It develops a novel semiparametric framework for mixed graphical models and proposes a symmetry-aware hypothesis test for edge presence, improving practical applicability and inference robustness.

Findings

The model effectively handles high-dimensional mixed data.

The symmetric score test accurately detects edges in the graph.

Numerical simulations and real data validate the method's performance.

Abstract

We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be semiparametric generalized linear models with unspecified base measure functions. Thus, one advantage of our method is that it is unnecessary to specify the type of each node and the method is more convenient to apply in practice. Under the proposed model, we consider both problems of parameter estimation and hypothesis testing in high dimensions. In particular, we propose a symmetric pairwise score test for the presence of a single edge in the graph. Compared to the existing methods for hypothesis tests, our approach takes into account of the symmetry of the parameters, such that the inferential results are invariant with respect to the different parametrizations of the same edge. Thorough numerical simulations and a real data example are provided to back up our results.