Kernel-Based Measures of Association

• Activity Number: 215
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): Ying Liu*+ and Victor de la Pena and Tian Zheng
• Companies: Columbia University and Columbia University and Columbia University
• Keywords: association measures ; association mining ; distance covariance ; kernel distances

Abstract

Numerical measures of association are important summary for describing statistical relationships between two sets of variables. Traditionally, such association measures were proposed and studied under specific settings, which has limited their use in applying to complex and high dimensional data. In this paper, we introduce a general framework for association measures that includes most commonly used conventional measures. It further allows novel and intuitive extensions based on kernels. Under this framework, we introduce association mining and variable screening via the maximization of the proposed kernel-based association measures. Several practical tactics are combined to overcome the computational challenges, especially when the dimension of the data under study is high. We evaluate our proposed framework by conducting independence tests and feature screening using kernel-based association measures on both simulated and real-world data with association patterns of different dimensions and variable types. Our results demonstrate the superiority of our method over existing methods and the ability for association mining for complex data in their most natural form.