# Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting

arXiv: https://arxiv.org/abs/1711.00950 · HTML: https://mlsanity.com/paper/1711.00950/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2017.

## Built on by (most cited first, 15 of 15)

- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov Networks](https://mlsanity.com/paper/2305.11379/) (2023)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
- [Ensemble transport smoothing. Part I: Unified framework](https://mlsanity.com/paper/2210.17000/) (2022)
- [Localized Diffusion Models](https://mlsanity.com/paper/2505.04417/) (2025)
- [Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matrices](https://mlsanity.com/paper/2107.04136/) (2021)
- [Learning Causal Graphs via Monotone Triangular Transport Maps](https://mlsanity.com/paper/2305.18210/) (2023)
- [Stein's method for marginals on large graphical models](https://mlsanity.com/paper/2410.11771/) (2024)
- [Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences](https://mlsanity.com/paper/2309.15366/) (2023)
- [Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach](https://mlsanity.com/paper/2503.13899/) (2025)
- [Causal Order Discovery based on Monotonic SCMs](https://mlsanity.com/paper/2410.19870/) (2024)
- [Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation](https://mlsanity.com/paper/2609.36142/) (2026)
- [Conditional Independence Estimates for the Generalized Nonparanormal](https://mlsanity.com/paper/2508.11050/) (2025)

## Abstract (arXiv)

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another.