Efficient Neural Causal Discovery without Acyclicity Constraints (2107.10483v3)

Abstract: Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which, however, require constrained optimization to enforce acyclicity or lack convergence guarantees. In this paper, we present ENCO, an efficient structure learning method for directed, acyclic causal graphs leveraging observational and interventional data. ENCO formulates the graph search as an optimization of independent edge likelihoods, with the edge orientation being modeled as a separate parameter. Consequently, we can provide convergence guarantees of ENCO under mild conditions without constraining the score function with respect to acyclicity. In experiments, we show that ENCO can efficiently recover graphs with hundreds of nodes, an order of magnitude larger than what was previously possible, while handling deterministic variables and latent confounders.

• The paper introduces ENCO, a method that models edge orientations individually to efficiently uncover causal structures from both observational and interventional data.
• It leverages low-variance gradient estimators to achieve scalable and precise learning in graphs with thousands of variables.
• The approach robustly handles partial interventions and detects latent confounders, enhancing its applicability in complex, real-world datasets.

Efficient Neural Causal Discovery without Acyclicity Constraints

The paper introduces ENCO, a novel method for causal discovery in directed acyclic graphs (DAGs) using both observational and interventional data without needing explicit acyclicity constraints. Causal discovery, which involves identifying the causal structure underlying a set of variables, is crucial in fields such as computational biology, epidemiology, and economics. Traditional approaches often face challenges in scaling to large graphs and ensuring convergence due to complex constraints like acyclicity.

Key Contributions

1. Parameterized Edge Orientation: ENCO innovatively models the orientation of each edge in the causal graph with a separate parameter, diverging from conventional methods that embed acyclicity constraints directly in their optimization processes. This differentiation provides ENCO with distinctive leverage to handle larger causal graphs efficiently.
2. Low-Variance Gradient Estimators: The method utilizes unbiased, low-variance gradient estimators for learning the graph parameters, a strategic move crucial for scaling the model to accommodate graphs with a large number of variables. This framework is particularly significant as it sidesteps the computational inefficiencies often encountered in existing constrained optimization strategies.
3. Robustness with Partial Interventions: The model's robustness extends to scenarios where interventions are not possible for all variables. The algorithm still performs admirably, showcasing its adaptability and practical applicability in real-world settings where data may be incomplete.
4. Latent Confounder Detection: ENCO introduces an extension for identifying latent confounders—unobserved variables influencing two or more observed variables. The ability to detect such confounders enhances the reliability of the resulting causal graphs, crucial for accurate causal interpretations.

Experimental Insights

ENCO was rigorously tested on a diverse array of graph structures, from those with minimal connectivity (e.g., chains) to fully connected graphs, achieving superior results compared to state-of-the-art methods like GIES, IGSP, SDI, and DCDI. Its performance was especially remarkable with datasets including thousands of nodes, where traditional methods falter due to scaling issues.

• Performance Metrics: Across multiple benchmarks, ENCO consistently outperformed competing algorithms in terms of structural hamming distance (SHD) and structural intervention distance (SID), which quantify the accuracy of causal discovery methods.
• Scalability: ENCO demonstrated its ability to learn causal structures from graphs with up to 1000 variables, an order of magnitude improvement over existing approaches.
• Efficiency: The experiments highlight the efficiency of ENCO, often achieving results with minimal errors within shorter computational times compared to baselines.

Implications and Future Directions

The implications of this research are notably broad, impacting both theoretical and applied aspects of causal inference:

• Scalability Without Sacrificing Complexity: ENCO's framework, marked by its avoidance of direct acyclicity constraints, sets a precedence in making causal discovery scalable without simplifying the underlying complexity that real-world data demands.
• Improved Practical Utility: By enabling causal discovery in large datasets and in the presence of latent confounders, ENCO widens the applicability of causal inference methodologies in areas such as genomics and large-scale epidemiological studies.

This research also opens several avenues for future work, including refining the model to handle even larger graphs efficiently, advancing transitive relations among orientation parameters, and extending guarantees to partial intervention scenarios. Additionally, exploring the integration of faithfulness assumptions or employing alternative data characterizations could further enhance ENCO's applicability and accuracy in various complex settings.

In conclusion, ENCO represents a significant stride in causal discovery, blending robust theoretical underpinnings with practical adaptability, illustrating a promising leap towards effective and scalable causal inference in complex domains.