Heavy-tailed disturbance models improve causal graph learning accuracy
DAG Structure Learning with Node-Varying Heavy-Tailed Disturbances
Machine Learning
Summary
Learning cause-and-effect relationships between things often assumes that the random noise in data follows a bell curve, which isn’t always true. This paper introduces a method that better handles different kinds of noise that can have heavy tails, meaning extreme values happen more often than with a bell curve. The authors developed an approach that figures out both the graph structure and the noise characteristics for each variable. Their tests show this method recovers the correct structure better in simulated data and fits financial data better than previous methods.
What this means in practice
- •For financial data teams: Improve causal structure discovery in financial datasets with non-Gaussian heavy-tailed noise patterns to enable better risk modeling.
- •For signal processing engineers: Enhance system identification when measurement noise varies across sensors and exhibits heavy tails, improving filter design and fault detection.
Authors
Robin Francis, Sundeep Prabhakar Chepuri
Abstract
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.