Kernel-based association measures

Measures of associations have been widely used for describing the statistical relationships between two sets of variables. Traditional association measures tend to focus on specialized settings (specific types of variables or association patterns). Based on an in-depth summary of existing measures, we propose a general framework for association measures unifying existing methods and novel extensions based on kernels, including practical solutions to computational challenges. The proposed framework provides improved feature selection and extensions to a variety of current classifiers. Specifically, we introduce association screening and variable selection via maximizing kernel-based association measures. We also develop a backward dropping procedure for feature selection when there are a large number of candidate variables. We evaluate our framework using a wide variety of both simulated and real data. In particular, we conduct independence tests and feature selection using kernel association measures on diversified association patterns of different dimensions and variable types. The results show the superiority of our methods to existing ones. We also apply our framework to four real-word problems, three from statistical genetics and one of gender prediction from handwriting. We demonstrate through these applications both the de novo construction of new kernels and the adaptation of existing kernels tailored to the data at hand, and how kernel-based measures of associations can be naturally applied to different data structures including functional input and output spaces. This shows that our framework can be applied to a wide range of real world problems and work well in practice.