# Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach

arXiv: https://arxiv.org/abs/2503.13899 · HTML: https://mlsanity.com/paper/2503.13899/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [On the representation and learning of monotone triangular transport maps](https://mlsanity.com/paper/2009.10303/) (2020)
- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)
- [Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matrices](https://mlsanity.com/paper/2107.04136/) (2021)

## Built on by (most cited first, 2 of 2)

- [Localized Diffusion Models](https://mlsanity.com/paper/2505.04417/) (2025)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)

## Abstract (arXiv)

Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical model, which encodes these dependencies, by assuming that the variables follow a distribution with a simple parametric form. Moreover, the computational cost of many algorithms scales poorly for high-dimensional distributions, as they need to estimate all the edges in the graph simultaneously. In this work, we propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property. The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps to represent the conditional distribution for each variable. We show that L-SING includes existing approaches, such as neighborhood selection with Lasso, as a special case. We demonstrate the effectiveness of our algorithm in both Gaussian and non-Gaussian settings by comparing it to existing methods. Lastly, we show the scalability of the proposed approach by applying it to high-dimensional non-Gaussian examples, including a biological dataset with more than 150 variables.