Auto-Tuning Kernel Mean Matching

The Kernel Mean Matching (KMM) algorithm is a mathematically rigorous method that directly weights the training samples such that the mean discrepancy in a kernel space is minimized. However, the applicability of KMM is still limited, due to the existence of many parameters that are difficult to adjust. This paper presents a novel method that automatically tunes the KMM parameters by assessing the quality of distribution matching from a new perspective. While the KMM itself minimizes the mean discrepancy in a reproducing kernel Hilbert space, the tuning of KMM is achieved by adopting a different quality measure which reflects the Normalized Mean Squared Error (NMSE) between the estimated importance weights and the ratio of the estimated test and training densities. This method enables the applicability of KMM to real domains and leads to a generalized routine for the KMM to incorporate different types of kernels. The effectiveness of the proposed method is demonstrated by experiments on both synthetic and benchmark datasets.