Learning high-dimensional directed acyclic graphs with latent and selection variables (1104.5617v3)

Abstract: We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI is slightly less informative, in particular with respect to conditional independence information. However, we prove that any causal information in the output of RFCI is correct in the asymptotic limit. We also define a class of graphs on which the outputs of FCI and RFCI are identical. We prove consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrate in simulations that the estimation performances of the algorithms are very similar. All software is implemented in the R-package pcalg.

• The paper introduces the RFCI algorithm, a novel approach that simplifies causal discovery in high-dimensional DAGs with latent and selection variables.
• It provides strong theoretical guarantees, ensuring accurate causal conclusions with reduced computational cost through selective conditional independence tests.
• Extensive simulations show that RFCI achieves performance comparable to FCI while significantly improving time efficiency in complex data scenarios.

Overview of the Paper: Learning High-Dimensional Directed Acyclic Graphs with Latent and Selection Variables

The paper under consideration presents a significant advancement in the field of causal structure learning, specifically addressing the complexities introduced by latent and selection variables in high-dimensional datasets. The research introduces the "Really Fast Causal Inference" (RFCI) algorithm, designed to efficiently infer causal structures in Directed Acyclic Graphs (DAGs) under conditions where traditional algorithms, such as the Fast Causal Inference (FCI) algorithm, become computationally infeasible due to the presence of these complicating factors.

Context and Motivation

In DAG-based causal inference, understanding the causal relationships among observed variables is crucial, especially in the presence of hidden confounders or selection bias. Traditional methods like FCI, although theoretically sound and complete, struggle with computational demands and efficiency in high-dimensional settings. The sheer size of possible conditioning sets leads to significant computational overhead.

Key Contributions and Methods

1. RFCI Algorithm: The introduction of the RFCI algorithm stands out as the primary contribution. This algorithm simplifies causal discovery in large, complex DAGs by focusing on a subset of conditional independence tests, thereby reducing computational demands. The trade-off is a potentially less informative output in terms of conditional independence, but the algorithm assures correct causal conclusions asymptotically.
2. Theoretical Guarantees: RFCI maintains the integrity of causal discovery through sound theoretical foundations, offering consistency under assumptions that allow for some degree of sparsity in the causal graphs. The paper proves that, despite simplifications, RFCI delivers results comparable to the intricately detailed outputs of the FCI algorithm.
3. Numerical Simulations: Extensive simulations demonstrate that RFCI performs comparably to FCI while being significantly more time-efficient. The simulations consider scenarios with varying graph sizes and latent variable presence, confirming the robustness and practicality of RFCI.
4. Comparative Analysis: The researchers also propose several adaptations to the FCI algorithm to improve its practicality, such as the Conservative FCI (CFCI) and Super-conservative FCI (SCFCI) algorithms. These adaptations are designed to mitigate some of FCI’s extensive computational requirements, hence providing a spectrum of algorithmic options based on the specific needs of the dataset or problem being tackled.

Implications and Future Directions

The implications of this research are twofold. Practically, RFCI opens doors to more efficient causal modeling in real-world, high-dimensional datasets where the time cost of current methods is prohibitive. Theoretically, it challenges the community to refine understanding and approaches to causal inference in the presence of numerous hidden variables, an area of growing importance given the complexity of modern data.

Future research might focus on exploring the boundaries of RFCI’s applicability, perhaps extending its capability to dynamically adapt to varying degrees of graph sparsity or integrating it into adaptive causal network learning frameworks. Additionally, efforts could aim at enhancing the comprehensiveness of the causal information inferred without significant computational trade-offs.

Conclusion

This paper makes substantial strides toward efficient causal inference in complex systems, addressing a critical bottleneck in the application of causal modeling to high-dimensional data. The introduction of RFCI alongside modifications to established algorithms presents a balanced approach to managing computational complexity while maintaining accurate causal inference capabilities. This work sets the stage for further exploration and refinement of causal modeling techniques in dynamic and opaque environments, driving forward the field of causal inference research.