Coarsening Causal DAG Models

arXiv stat.ML / 4/3/2026

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Key Points

The paper studies causal abstraction for Directed Acyclic Graph (DAG) models, addressing cases where causal structure cannot or should not be estimated at the finest feature level of a dataset.
It delivers new graphical identifiability results for interventional scenarios that are practically relevant to real-world causal inference.
The authors propose an efficient, provably consistent method to learn abstract causal graphs directly from interventional data even when intervention targets are unknown.
The work includes theoretical analysis of the lattice structure of the search space, linking the abstraction framework to broader causal discovery theory.
Experiments on synthetic and real datasets, including measurements from a controlled physical system involving interacting light intensity and polarization, provide proof-of-concept for the approach.

Abstract

Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always practical or desirable to estimate a causal model at the granularity of given features in a particular dataset. There is a growing body of research on causal abstraction to address such problems. We contribute to this line of research by (i) providing novel graphical identifiability results for practically-relevant interventional settings, (ii) proposing an efficient, provably consistent algorithm for directly learning abstract causal graphs from interventional data with unknown intervention targets, and (iii) uncovering theoretical insights about the lattice structure of the underlying search space, with connections to the field of causal discovery more generally. As proof of concept, we apply our algorithm on synthetic and real datasets with known ground truths, including measurements from a controlled physical system with interacting light intensity and polarization.