Integrating Biclustering and Causal Discovery for Data Relationships

Abstract

This work presents a novel methodology that integrates biclustering with causal analysis, incorporating Directed Acyclic Graph (DAG) constraints to ensure causal interpretability. The proposed approach is particularly effective in scenarios where it is important to identify causal relationships alongside cluster patterns, such as analyzing interactions among different groups in high-dimensional data. The method involves solving an optimization problem that balances biclustering accuracy with causal consistency while maintaining DAG constraints. To achieve this, we use a combination of matrix transformation, Stiefel manifold optimization for orthogonality, and an augmented Lagrangian method enhanced with edge swapping techniques inspired by previous works. We demonstrate how this approach can effectively discover latent group structures and directional influences between these groups, making it suitable for applications in biological and social data analysis where interpretability and stability are crucial. The inclusion of convex constraints ensures stability and computational efficiency, while the edge-swapping technique helps mitigate non-convexity challenges during optimization.