Beyond State Space Representation: A General Theory for Kernel Packets
School of Data Science, Fudan University（复旦大学数据科学学院）；Wm Michael Barnes ’64 Department of Industrial & Systems Engineering Texas A&M University（德克萨斯大学阿姆斯特朗分校工业与系统工程系）；School of Management, Shenzhen Polytechnic University（深圳职业技术大学管理学院）
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve linear-time inference by reformulating GPs as stochastic differential equations (SDEs). However, SS approaches are confined to gridded inputs and cannot handle multi-dimensional scattered data. We propose a new framework based on kernel packet (KP), which overcomes these limitations while retaining exactness and scalability. A KP is a compactly supported function defined as a linear combination of the GP covariance functions. In this article, we prove that KPs can be identified via the forward and backward SS representations. We also show that the KP approach enables exact inference with linear-time training and logarithmic or constant-time prediction, and extends naturally to multi-dimensional gridded or scattered data without low-rank approximations. Numerical experiments on large-scale additive and product-form GPs with millions of samples demonstrate that KPs achieve exact, memory-efficient inference where SDE-based and low-rank GP methods fail.
Estimation Beyond Data Reweighting: Kernel Method of Moments
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机学研究所）；Eidgenössische Technische Hochschule Zürich（苏黎世联邦理工学院）
Efficient Global String Kernel with Random Features: Beyond Counting Substructures
IBM Research（IBM研究院）；Carnegie Mellon University（卡内基梅隆大学）；George Mason University（乔治梅森大学）；Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies（阿里巴巴-浙江大学前沿技术联合研究院）；Zhejiang University（浙江大学）
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）
Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descents
Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University, Xi’an, China（智能决策与机器学习中心，管理学院，西安交通大学，西安，中国）；Department of Mathematics, The University of Hong Kong, Hongkong, China（数学系，香港大学，香港，中国）
