On Semiparametric Exponential Family Graphical Models
This work addresses the challenge of analyzing mixed data in graphical models for researchers in statistics and machine learning, offering a more flexible and convenient method, though it is incremental as it builds on existing mixed graphical models.
The authors tackled the problem of modeling high-dimensional mixed data by proposing a new class of semiparametric exponential family graphical models that do not require specifying node types, making them more practical. They developed methods for parameter estimation and hypothesis testing, including a symmetric pairwise score test for edge detection, and validated their approach with simulations and a real data example.
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.