Efficient Differentiable Discovery of Causal Order (2410.08787v1)

Abstract: In the algorithm Intersort, Chevalley et al. (2024) proposed a score-based method to discover the causal order of variables in a Directed Acyclic Graph (DAG) model, leveraging interventional data to outperform existing methods. However, as a score-based method over the permutahedron, Intersort is computationally expensive and non-differentiable, limiting its ability to be utilised in problems involving large-scale datasets, such as those in genomics and climate models, or to be integrated into end-to-end gradient-based learning frameworks. We address this limitation by reformulating Intersort using differentiable sorting and ranking techniques. Our approach enables scalable and differentiable optimization of causal orderings, allowing the continuous score function to be incorporated as a regularizer in downstream tasks. Empirical results demonstrate that causal discovery algorithms benefit significantly from regularizing on the causal order, underscoring the effectiveness of our method. Our work opens the door to efficiently incorporating regularization for causal order into the training of differentiable models and thereby addresses a long-standing limitation of purely associational supervised learning.

• The paper introduces DiffIntersort, a differentiable algorithm that refines Intersort for efficient causal order discovery using gradient-based optimization.
• It demonstrates scalability and robustness on simulated datasets across linear models, gene regulatory networks, and random Fourier features.
• The approach integrates a potential function as a regularizer, offering theoretical guarantees linking potential maximization with accurate causal ordering.

Efficient Differentiable Discovery of Causal Order

The paper "Efficient Differentiable Discovery of Causal Order" by Mathieu Chevalley, Arash Mehrjou, and Patrick Schwab presents advancements in the field of causal discovery by expanding capabilities within Directed Acyclic Graphs (DAGs). Specifically, it offers an enhanced approach to the differentiable discovery of causal orders, building on the challenges and limitations of a previous algorithm called Intersort. It aligns with a significant need in causal inference, relevant across diverse applications including genomics and climate modeling.

Overview of Intersort Limitations and New Approach

Intersort was initially designed to infer causal orders by leveraging interventional datasets, marking an improvement over traditional observational data-dependent methods. Despite its strengths, it lacked scalability and computational efficiency—critical drawbacks when addressing datasets common in genomics and other fields with thousands of variables. The present work refines Intersort, introducing a framework built on differentiable sorting and ranking methodologies, such as employing the Sinkhorn operator. This new approach, named DiffIntersort, reformulates the Intersort score to make it compatible with gradient-based optimization frameworks.

Empirical and Methodological Contributions

The authors make several substantive empirical contributions. They demonstrate that the DiffIntersort algorithm can handle significantly larger datasets compared to its predecessor. The assessment proceeds through simulated datasets reflecting linear, gene regulatory network, and random Fourier features models. The refined algorithm demonstrates superior performance to established methods like GIES and DCDI, specifically in terms of robustness across different noise types and scaling efficiency.

The methodology posits using a potential function to express the score for a causal order. This articulation enhances scalability and allows integration as a regularizer in downstream machine learning models. Theoretical guarantees provided within the text assert that the potential coincides with causal ordering, backed by proof linking potential maximization with causal order maximization.

Implications and Future Prospects

This paper represents an advancement towards efficiently utilizing interventional data for causal inference in large-scale settings. By bridging causality with differentiable optimization principles, it opens possibilities for incorporating causal discovery into complex models, including those encompassing deep learning architectures.

Practically, the research augments the implementation of modern causal learning pipelines by alleviating scalability bottlenecks in previous methods. As differential causal discovery gains traction, applications spanning genomics, neuroscience, and environmental science could benefit significantly from these innovations.

Future avenues might include adapting the differentiable Intersort approach further into deep learning environments and exploring real-world datasets where large-scale interventional data is routinely available, such as within genomics and medical data platforms. Overall, this work underscores a direction of high relevance in advancing causal machine learning methodologies.