Problem
Research questions and friction points this paper is trying to address.
Directed Acyclic Graph (DAG)
Latent Variables
Causal Discovery
Non-Gaussian Measurement Models
DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables
🤖 AI Summary
This study addresses the challenges of learning causal directed acyclic graphs (DAGs) with latent variables and non-Gaussian observational data, which are hindered by high-dimensional integration bottlenecks and structural identifiability issues. To overcome these limitations, this work proposes DAG-CLIP, a novel framework that introduces a composite likelihood screening and iterative pruning mechanism tailored for latent variables. By integrating smooth acyclicity-constrained optimization, BIC-guided backward elimination, and Markov equivalence class search, the method achieves effective synergy between continuous optimization and discrete search. Theoretically, DAG-CLIP resolves the computational bottleneck while guaranteeing statistical consistency. Empirically, it successfully recovers true sparse causal structures on both simulated datasets and large-scale educational surveys, demonstrating its efficiency and effectiveness in practice.
📝 Abstract
Learning directed acyclic graphs (DAGs) to uncover causal mechanisms has attracted substantial attention in machine learning. While most existing methods focus exclusively on observed variables, many variables of substantive interest are latent constructs defined by statistical measurement models. Such constructs are particularly common in the social and behavioral sciences. In this paper, we propose a general statistical framework for DAG learning when some or all nodes of the graph are latent variables, accommodating non-Gaussian manifest variables such as binary and categorical data in the measurement model. To overcome the computational burden of high-dimensional integration in standard marginal likelihoods, we develop DAG learning via Composite-Likelihood-based screening and Iterative Pruning (DAG-CLIP), a two-step composite-likelihood-based learning algorithm. This algorithm first solves a smooth acyclicity-constrained optimization problem to screen out misspecified DAG structures, and subsequently performs BIC-guided composite-likelihood backward deletion within the Markov equivalence class (MEC) space to identify a sparse DAG. We establish the statistical consistency of the algorithm in recovering the MEC of the true DAG, and demonstrate its effectiveness through extensive simulation studies and a real-world application to large-scale educational survey data.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Directed Acyclic Graph
Latent Variables
Composite Likelihood
Causal Discovery
Non-Gaussian Data
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