Reproducing Kernels for Pairwise Learning

• Activity Number: 487 - Neural Networks, Deep Learning, and RKHS
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xin Guo* and Ting Hu and Qiang Wu and Ding-Xuan Zhou
• Companies: The Hong Kong Polytechnic University and Wuhan University and Middle Tennessee State University and City University of Hong Kong
• Keywords: pairwise learning; reproducing kernels; learning theory

Abstract

Pairwise learning is a large family of learning algorithms for the problems where supervised labels are not available, but one has only the access to the differences between labels of each pair of sample points. For example, ranking, AUC maximization, metric learning, gradient learning, and so on. We studied a transform of reproducing kernels so that the reproducing kernel Hilbert space defined by the obtained kernel lies in the orthogonal complement of constant functions, and is thus a perfect hypothesis space for learning the scoring functions. We proved that the kernel space complexity is invariant after this transformation. We also obtained some relations between the integral operators before and after the kernel transformation.