Hilbert Schmidt Independence Criterion

The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel-based measure quantifying the dependence between random variables, primarily used for independence testing and feature selection. Current research focuses on improving HSIC's efficiency and robustness, particularly addressing limitations in kernel selection, developing more efficient estimators (like Nyström-based methods and incomplete U-statistics), and applying HSIC within various machine learning contexts, including deep learning architectures (e.g., GRU networks) and causal inference. HSIC's significance lies in its ability to detect non-linear dependencies and its broad applicability across diverse fields, from out-of-distribution detection and model explainability to robustness against adversarial attacks and improved hyperparameter optimization.