Demistifying Data and Simulator Assumptions in Supervised Causal Discovery

2026-09-29

AI Summary

This study addresses the unclear impact of simulator assumptions and the frequent conflation of identifiability with out-of-distribution generalization in supervised causal discovery. To this end, it constructs a multidimensional taxonomy encompassing encoders, structural decoders, and training paradigms to systematically analyze how data and simulator assumptions complement observational information. Furthermore, this work proposes a novel paradigm that aligns evaluation metrics with identifiable graph targets, revealing the risk of spurious precision arising from mechanistic limitations. Ultimately, it establishes an analytical framework for guiding method comparisons and identifies key open problems in transfer learning, test-time adaptation, and uncertainty quantification. Collectively, these contributions provide a rigorous theoretical foundation for evaluating causal discovery methods.

Abstract

Supervised causal discovery learns to infer causal structure for a new dataset from training datasets paired with structural labels. These training pairs are typically simulated, making the simulator both a source of supervision and a carrier of assumptions about causal graphs, mechanisms, and noise. Understanding the resulting predictions therefore requires examining how these assumptions supplement the information available in observational data, which may be compatible with multiple causal graphs. This paper examines that relationship across representative methods available through June 2026. We organize these methods by prediction target, prediction granularity, encoder, structural decoder, and training regime to relate what each method predicts to how it uses data and simulator-based supervision. Using this framework, we distinguish two questions: whether the target is identifiable under the assumed model class, and whether a trained predictor generalizes beyond its training distribution. Restrictions on mechanisms and noise can make otherwise ambiguous causal directions identifiable, but predictive accuracy under those restrictions does not establish transfer when they change. This distinction motivates evaluation that matches metrics to the identifiable graph target and tests changes in graphs, mechanisms, and noise between training and deployment. Extending such evaluation to real data also requires documenting the external causal evidence and uncertainty behind benchmark reference graphs. Together, these analyses guide method comparison and identify open questions in transfer, test-time adaptation, and uncertainty assessment.

Problem

• Supervised Causal Discovery
• Simulator Assumptions
• Identifiability
• Generalization
• Evaluation

Innovation

• Supervised Causal Discovery
• Identifiability
• Generalization
• Simulator Assumptions
• Evaluation Framework