A1272
Title: Adaptive independence test via the generalized HSIC
Authors: Yaowu Zhang - Shanghai University of Finance and Economics (China) [presenting]
Abstract: Measuring and testing for nonlinear dependence between random vectors is a fundamental problem in the statistics and machine learning literature. Among various measures, the Hilbert-Schmidt independence criterion (HSIC) has garnered significant attention due to its theoretical and computational advantages. We analyze the traditional HSIC in depth and establish a connection between HSIC and the distance correlation. We reveal that it mainly detects linear dependencies and approaches zero when the dimensions grow, with the leading factor being the aggregation of linear dependencies. To improve the sensitivity of HSIC to nonlinear dependencies, we propose the Generalized HSIC (GHSIC), which has a closed-form expression and equals zero if and only if the two random vectors are independent. Through our investigation, we demonstrate that GHSIC effectively overcomes the limitations of HSIC and exhibits enhanced capability in detecting nonlinear dependencies, particularly in high-dimensional settings. Furthermore, we develop a data-adaptive test based on GHSIC, which outperforms the HSIC-based test in high-dimensional scenarios, even when linear dependencies are present. Extensive numerical experiments demonstrate the superiority of the proposed GHSIC.
