Learning Linear Non-Gaussian Polytree Models

TL;DR

This paper introduces efficient algorithms for learning polytree structures in linear non-Gaussian causal models, combining the Chow--Liu method with novel orientation schemes based on distribution moments, supported by theoretical consistency and empirical evaluation.

Contribution

It presents a new approach for learning polytrees in LiNGAMs by integrating Chow--Liu with moment-based orientation schemes, with proven high-dimensional consistency.

Findings

Algorithms accurately recover polytrees in simulations

Orientation schemes are computationally inexpensive

High-dimensional consistency is established

Abstract

In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow--Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.