# On Semiparametric Exponential Family Graphical Models

arXiv: https://arxiv.org/abs/1412.8697 · HTML: https://mlsanity.com/paper/1412.8697/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2014.

## Built on by (most cited first, 6 of 6)

- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
- [On Computationally Efficient Learning of Exponential Family Distributions](https://mlsanity.com/paper/2309.06413/) (2023)
- [Nonparanormal Graph Quilting with Applications to Calcium Imaging](https://mlsanity.com/paper/2305.13491/) (2023)
- [High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data](https://mlsanity.com/paper/2211.11700/) (2022)
- [Discrete Score Matching Enables Causal Discovery from Count Data](https://mlsanity.com/paper/2609.39326/) (2026)

## Abstract (arXiv)

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.