Independence Testing

Independence testing, a core statistical problem, aims to determine whether two or more variables are statistically independent. Current research focuses on developing robust and efficient tests, particularly for high-dimensional data and complex relationships, employing methods like kernel-based approaches (e.g., HSIC, distance covariance), permutation tests, and optimal transport techniques. These advancements are crucial for various applications, including causal inference, feature selection in machine learning, and ensuring data privacy in machine unlearning, by enabling more accurate and reliable assessments of variable relationships in diverse data settings. Furthermore, research is addressing the challenges of testing independence in non-i.i.d. data and under distributional shifts.