An information-theoretic approach for heterogeneous differentiable causal discovery

With the advancement of deep learning, a variety of differential causal discovery methods have emerged, inevitably attracting more attention for their excellent scalability and interpretability. However, these methods often struggle with complex heterogeneous datasets that exhibit environmental diversity and are characterized by shifts in noise distribution. To this end, we introduce a novel information-theoretic approach designed to enhance the robustness of differential causal discovery methods. Specifically, we integrate Minimum Error Entropy (MEE) as an adaptive error regulator into the structure learning framework. MEE effectively reduces error variability across diverse samples, enabling our model to adapt dynamically to varying levels of complexity and noise. This adjustment significantly improves the precision and stability of the model. Extensive experiments on both synthetic and real-world datasets have demonstrated significant performance enhancements over existing methods, affirming the effectiveness of our approach. The code is available at https://github.com/ElleZWQ/MHCD.