Personalized Binomial DAGs Learning with Network Structured Covariates

TL;DR

This paper introduces personalized Binomial DAG models for causal discovery in multivariate count data, addressing user heterogeneity and social network dependencies, with an algorithm that improves learning accuracy over existing methods.

Contribution

The paper proposes a novel personalized Binomial DAG model and an efficient learning algorithm that incorporates network structure and heterogeneity, advancing causal discovery in complex data.

Findings

The algorithm outperforms state-of-the-art methods in simulations.

It effectively captures heterogeneity and network dependencies.

Practical application on web visit data demonstrates usefulness.

Abstract

The causal dependence in data is often characterized by Directed Acyclic Graphical (DAG) models, widely used in many areas. Causal discovery aims to recover the DAG structure using observational data. This paper focuses on causal discovery with multi-variate count data. We are motivated by real-world web visit data, recording individual user visits to multiple websites. Building a causal diagram can help understand user behavior in transitioning between websites, inspiring operational strategy. A challenge in modeling is user heterogeneity, as users with different backgrounds exhibit varied behaviors. Additionally, social network connections can result in similar behaviors among friends. We introduce personalized Binomial DAG models to address heterogeneity and network dependency between observations, which are common in real-world applications. To learn the proposed DAG model, we develop an algorithm that embeds the network structure into a dimension-reduced covariate, learns each node's neighborhood to reduce the DAG search space, and explores the variance-mean relation to determine the ordering. Simulations show our algorithm outperforms state-of-the-art competitors in heterogeneous data. We demonstrate its practical usefulness on a real-world web visit dataset.