# DAG Structure Learning with Node-Varying Heavy-Tailed Disturbances

arXiv: https://arxiv.org/abs/2610.13304 · HTML: https://mlsanity.com/paper/2610.13304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Causal discovery in heavy-tailed models](https://mlsanity.com/paper/1908.05097/) (2019)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Effective Causal Discovery under Identifiable Heteroscedastic Noise Model](https://mlsanity.com/paper/2312.12844/) (2023)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [Robust Graphical Modeling with t-Distributions](https://mlsanity.com/paper/1408.2033/) (2014)

## Abstract (arXiv)

DAG structures can be learned from observations by incorporating acyclicity via smooth constraints, such as DAGMA's log-determinant function. Typically, observations and the underlying DAG are related through linear structural equation models, with Gaussianity assumption on the disturbances at each node. Extending DAG learning methods that account for scale and tail behavior of disturbances that vary across nodes remains a challenge. We propose a node-varying Student-t DAGMA that jointly estimates the graph structure, node-specific disturbance scales, and the degrees-of-freedom parameter. A Gaussian scale-mixture representation yields an iteratively reweighted formulation that down-weights large standardized residuals. Building on existing results, we also establish identifiability of the graph and disturbance parameters. Synthetic experiments demonstrate improved structural recovery under heterogeneous heavy-tailed disturbances, and experiments on real finance data show that the proposed method yields lower test negative log-likelihood than the evaluated baselines.