Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers
This work addresses the computational bottleneck in learning flexible non-Gaussian DAG models for applications such as statistics and sales analysis, though it is incremental in nature.
The paper tackles the problem of learning directed acyclic graphs (DAGs) for non-Gaussian models with quadratic variance functions, introducing topological layers to develop an efficient algorithm that reduces computational cost compared to existing methods, as demonstrated in simulations and real-world datasets like NBA statistics and Alibaba sales data.
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.