Kweku Opoku-Agyemang
Working Paper Class 58
This paper introduces a novel theoretical framework for generative causal models, which integrates Flow Matching, a state-of-the-art generative modeling technique, with causal inference to address the challenge of generating data that inherently respects causal structures. We propose a mathematical formulation where Flow Matching, defined by a vector field that transports noise to data along a specified path, is constrained by causal graphs to ensure that the generated samples adhere to causal relationships. Specifically, we consider a directed acyclic graph, representing variables and their causal dependencies, and define a generative process consistent with this graph. The Flow Matching objective is adapted to minimize the discrepancy between the learned vector field and a target vector field derived directly from the causal structure. We prove that under certain regularity conditions, the optimized vector field converges to this target, ensuring that the generated samples are causally consistent. Furthermore, we extend this framework to handle interventional and counterfactual scenarios by defining conditional Flow Matching objectives that respect do-calculus operations. For an intervention, the generative process is modified to align with the post-interventional distribution, and we derive bounds on the approximation error in terms of the causal graph’s structure and the Flow Matching model’s capacity. This theoretical advancement not only enhances the interpretability and robustness of generative models but also provides a new tool for causal discovery and policy analysis in high-dimensional settings. Our results suggest that generative causal models can significantly improve the estimation of causal effects in complex systems, offering a unified approach to generation and inference that is both theoretically grounded and practically scalable.
The views in this Working Paper Class are those of the authors, not necessarily of Machine Learning X Doing.
Opoku-Agyemang, Kweku A. (2025). "Generative Causal Models: A Theoretical Framework for Integrating Flow Matching and Causal Inference." Machine Learning X Doing Working Paper Class 58. Machine Learning X Doing.
Copyright © 2025 Machine Learning X Doing Incorporated. All Rights Reserved.
