Differentiable Causal Discovery from Interventional Data (2007.01754v2)

Abstract: Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous constrained optimization one, which is solved via the augmented Lagrangian method. However, most methods based on this idea do not make use of interventional data, which can significantly alleviate identifiability issues. This work constitutes a new step in this direction by proposing a theoretically-grounded method based on neural networks that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.

• The paper introduces DCDI, a novel differentiable framework leveraging neural networks and various types of interventional data for causal structure learning.
• The framework offers theoretical guarantees for identifying the graph up to its interventional Markov equivalence class, improving identifiability over observational methods.
• Empirical comparisons show DCDI performs competitively across various settings and model complexities, with potential practical applications in fields like genomics.

Differentiable Causal Discovery from Interventional Data

The paper "Differentiable Causal Discovery from Interventional Data" presents a novel approach to causal discovery using interventional data with a differentiable framework. The authors address the problem of learning causal directed acyclic graphs (DAGs) from data, which is fundamental to understanding causal relationships in various scientific domains. Traditionally, causal discovery from observational data is challenging due to identifiability issues arising from the faithfulness assumption, which limits the identifiability to a Markov equivalence class. However, the utilization of interventional data, where experiments are systematically conducted, can significantly enhance identifiability by narrowing it down to an interventional Markov equivalence class.

Main Contributions

The paper introduces Differentiable Causal Discovery with Interventions (DCDI), an innovative method that leverages neural networks for causal structure learning. Key contributions include:

• DCDI Framework: A general differentiable causal structure learning approach leveraging perfect, imperfect, and unknown-target interventions. The framework builds on expressive neural architectures like normalizing flows, which offer a flexible alternative to linear models.
• Identifiability Guarantees: The authors demonstrate that maximizing the proposed score will identify the $\mathcal{I}$-Markov equivalence class of the ground truth graph under regularity conditions for both known and unknown-target settings.
• Empirical Comparison: Extensive experiments are conducted comparing DCDI to various state-of-the-art methods in different settings, including multiple functional forms and types of interventions. DCDI showed competitive performance, particularly in settings with higher model complexity and number of interventions.

Theoretical Foundations

DCDI is grounded in theoretical guarantees that ensure identifiability of the causal graph up to the $\mathcal{I}$-Markov equivalence class. The paper extends the work by reformulating the causal discovery problem as a continuous constrained optimization problem, which enables the use of gradient-based optimization methods. This approach effectively avoids the combinatorial search typical of score-based methods.

Practical Implications and Future Directions

The DCDI framework promises practical implications for fields like genomics, where high-throughput interventional data are prevalent. Its effective use of interventional data could facilitate more accurate modeling of gene regulatory networks. Furthermore, DCDI's use of expressive models like normalizing flows suggests future research directions in enhancing model capacity for complex causal relationships. The framework's compatibility with extensive data sets also opens avenues for scaling causal discovery processes to larger systems.

Conclusion

The paper presents a robust, scalable framework for causal discovery with the ability to leverage interventional data and complex neural architectures. DCDI compares favorably against existing methods under various conditions, with potential applications spanning multiple scientific and applied domains. This work invites further exploration in enhancing model capacity and application to diverse types of data, including time-series and context-variable settings. As artificial intelligence continues to evolve, frameworks like DCDI offer promising pathways for integrating causal inference into machine learning and broader scientific investigations.