[Paper Review] D'ya like DAGs? A Survey on Structure Learning and Causal Discovery

Matthew J. Vowels, Necati Cihan Camgöz+1 more|arXiv (Cornell University)|Mar 3, 2021

Computational Drug Discovery Methods4 citations

TL;DR

This survey provides a comprehensive overview of modern structure learning and causal discovery methods, focusing on continuous optimization techniques for learning directed acyclic graphs (DAGs) from observational data. It highlights key assumptions, evaluates common metrics, and emphasizes the critical distinction between graphical structure and true causality, cautioning against uncritical interpretation of learned models as causal realities.

ABSTRACT

Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure discovery. We primarily focus on modern, continuous optimization methods, and provide reference to further resources such as benchmark datasets and software packages. Finally, we discuss the assumptive leap required to take us from structure to causality.

Motivation & Objective

• To provide a thorough review of modern structure learning and causal discovery methods, particularly those based on continuous optimization.
• To clarify the assumptions and limitations underlying causal interpretation of learned DAGs, especially the Causal Markov Condition and structural equation models.
• To address the critical gap between identifying graphical structure and asserting true causality, highlighting risks of misinterpretation.
• To guide researchers by compiling benchmark datasets, software tools, and resources for further study and implementation.
• To encourage cautious, principled use of causal discovery methods, especially in high-stakes domains like healthcare and policy.

Proposed method

• Focuses on continuous optimization approaches for DAG structure learning, replacing discrete search over DAGs with differentiable optimization over adjacency matrices.
• Employs differentiable relaxation techniques such as the Gumbel-Softmax or continuous relaxation of the DAG constraint to enable gradient-based optimization.
• Utilizes score-based methods that optimize a differentiable score function (e.g., likelihood or BIC) under the constraint that the resulting graph is a DAG.
• Applies techniques like the sparsemax or relaxation of the acyclicity constraint using the trace trick (e.g., Tr(I - A)^{-1} for adjacency matrix A).
• Reviews methods that combine observational and interventional data to improve identifiability and causal structure recovery.
• Outlines evaluation metrics such as F1-score, structural Hamming distance, and precision/recall for DAG structure comparison.

Experimental results

Research questions

• RQ1 How can continuous optimization methods effectively learn DAG structures from observational data while enforcing acyclicity?
• RQ2 What are the key assumptions—especially the Causal Markov Condition—underlying the interpretation of learned DAGs as causal models?
• RQ3 To what extent can structure discovery methods reliably recover true causal relationships without experimental interventions?
• RQ4 What are the limitations and risks of interpreting learned graphical structures as causal, particularly in the presence of latent confounders or selection bias?
• RQ5 How can researchers responsibly use causal discovery tools, especially when the leap from structure to causality is not guaranteed?

Key findings

• Continuous optimization methods, particularly those using differentiable relaxation of the DAG constraint, enable efficient and scalable structure learning from observational data.
• The Causal Markov Condition is a foundational but untestable assumption that underpins the causal interpretation of DAGs, yet it does not guarantee that the graph reflects true causal mechanisms.
• Many structure discovery methods uncritically label themselves as 'causal' despite relying solely on conditional independence, which may mislead users about the validity of causal claims.
• The use of interventional data can improve identifiability and help distinguish between Markov equivalent DAGs, increasing confidence in causal structure recovery.
• Despite their utility, causal discovery methods risk reinforcing systemic biases if variables are poorly defined or if the model is interpreted as representing reality without critical scrutiny.
• The survey concludes that while causal discovery is a valuable tool for hypothesis generation and model interpretation, researchers must remain cautious and avoid conflating graphical structure with causal truth.