# On Graphical Models via Univariate Exponential Family Distributions

arXiv: https://arxiv.org/abs/1301.4183 · HTML: https://mlsanity.com/paper/1301.4183/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2013.

## Built on by (most cited first, 26 of 26)

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- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
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- [Feature Programming for Multivariate Time Series Prediction](https://mlsanity.com/paper/2306.06252/) (2023)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
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- [Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity](https://mlsanity.com/paper/2209.08273/) (2022)
- [Zero-Flow Encoders](https://mlsanity.com/paper/2602.00797/) (2026)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [On Computationally Efficient Learning of Exponential Family Distributions](https://mlsanity.com/paper/2309.06413/) (2023)
- [Causal Discovery with Generalized Linear Models through Peeling Algorithms](https://mlsanity.com/paper/2310.16698/) (2023)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [Thresholded Graphical Lasso Adjusts for Latent Variables: Application to Functional Neural Connectivity](https://mlsanity.com/paper/2104.06389/) (2021)
- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers](https://mlsanity.com/paper/2111.01560/) (2021)
- [Nonparanormal Graph Quilting with Applications to Calcium Imaging](https://mlsanity.com/paper/2305.13491/) (2023)
- [A Copula Graphical Model for Multi-Attribute Data using Optimal Transport](https://mlsanity.com/paper/2404.06735/) (2024)
- [Sequential Kernelized Stein Discrepancy](https://mlsanity.com/paper/2409.17505/) (2024)
- [Explainable Graph Theory-Based Identification of Meter-Transformer Mapping](https://mlsanity.com/paper/2205.09874/) (2022)
- [Meta Learning for High-dimensional Ising Model Selection Using ℓ1-regularized Logistic Regression](https://mlsanity.com/paper/2208.09539/) (2022)
- [A Unified Theory of Exact Inference and Learning in Exponential Family Latent Variable Models](https://mlsanity.com/paper/2404.19501/) (2024)
- [Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees](https://mlsanity.com/paper/2504.16356/) (2025)
- [Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data](https://mlsanity.com/paper/2609.01783/) (2026)
- [Causal Inference with Unobserved Confounding: A Mixture Learning Perspective](https://mlsanity.com/paper/2609.23219/) (2026)

## Abstract (arXiv)

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions.