Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers

TL;DR

This paper introduces a novel efficient algorithm for learning a special class of non-Gaussian DAG models with quadratic variance functions, leveraging topological layers to reduce computational complexity and improve accuracy.

Contribution

It proposes a new concept of topological layers and an efficient hierarchical learning algorithm for quadratic variance function DAGs, applicable to various distributions.

Findings

The algorithm accurately recovers DAG structures in simulated data.

It outperforms existing methods in computational efficiency.

Demonstrated successful application on real-world datasets.

Abstract

Directed acyclic graph (DAG) models are widely used to represent causal relationships among random variables in many application domains. This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean. Such a class of non-Gaussian DAG models are fairly flexible and admit many popular distributions as special cases, including Poisson, Binomial, Geometric, Exponential, and Gamma. To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm. It first reconstructs the topological layers in a hierarchical fashion and then recoveries the directed edges between nodes in different layers, which requires much less computational cost than most existing algorithms in literature. Its advantage is also demonstrated in a number of simulated examples, as well as its applications to two real-life datasets, including an NBA player statistics data and a cosmetic sales data collected by Alibaba.