Inference for a Large Directed Acyclic Graph with Unspecified Interventions.

Area of Science:

• Causal Inference
• Statistical Modeling
• Network Analysis

Background:

• Statistical inference of directed relationships is complicated by unknown intervention targets.
• Classical inference methods struggle with identifying ancestors and relevant interventions for hypothesis testing.
• Accurate causal discovery is crucial for understanding complex systems like gene regulatory networks.

Purpose of the Study:

• To develop a method for testing hypothesized directed relations with unspecified interventions.
• To establish conditions for model identifiability in causal inference with unknown interventions.
• To provide a robust statistical test accounting for uncertainties in identifying causal structures.

Main Methods:

• Proposed a peeling algorithm using nodewise regressions to determine a topological order of primary variables.
• Derived conditions for model identifiability, focusing on identifying ancestors and relevant interventions.
• Developed a likelihood ratio test combined with a data perturbation scheme for robust statistical inference.

Main Results:

• The peeling algorithm provides a consistent estimator in low-order polynomial time.
• The data perturbation test statistic's distribution converges to the target distribution, ensuring reliability.
• Numerical examples and a gene regulatory network application demonstrate the method's effectiveness.

Conclusions:

• The proposed methods effectively address the challenge of statistical inference with unspecified interventions.
• The developed algorithm and test offer a computationally efficient and statistically sound approach to causal discovery.
• This work contributes a valuable tool for inferring directed relationships in complex biological and statistical systems.