Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Oxford（牛津大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, Bharath K Sriperumbudur
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.
University of Manchester（曼彻斯特大学）；Universidad Tecnológica de Pereira（佩雷拉科技大学）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利理工学院）；University of Sheffield（谢菲尔德大学）；The Sheffield Institute for Translational Neuroscience（谢菲尔德转化神经科学研究所）
New Equivalences Between Interpolation and SVMs: Kernels and Structured Features
School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电子与计算机工程系）；Institute of Mathematics, EPFL（瑞士联邦理工学院数学学院）；School of Industrial & Systems Engineering, Georgia Institute of Technology（佐治亚理工学院工业与系统工程系）
Kernel Mean Embedding of Distributions: A Review and Beyond
Mahidol University（玛希隆大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Institute of Statistical Mathematics（统计数学研究所）；Pennsylvania State University（宾夕法尼亚州立大学）
Equivalence of distance-based and RKHS-based statistics in hypothesis testing
University College London（伦敦大学学院）；University of Cambridge（剑桥大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Institute of Statistical Mathematics（统计数学研究所）
