Sample Complexity of Kernel Methods for Machine Learning
葉行遠博士國立臺灣大學資料科學學位學程 15:30-17:00 Tòa nhà Hồng Kinh M107Abstract：
In this talk, I will discuss the theoretical analysis of the sample complexity of kernel methods in machine learning, with applications to manifold learning and reinforcement learning. In manifold learning, we introduce scalable landmark-based spectral algorithms, Landmark Alternating Diffusion (LAD) and Landmark Vector Diffusion Maps (LA-VDM), designed for sensor fusion and for capturing complex geometric structures,respectively.Under standard manifold assumptions, we present theoretical guarantees on consistency, convergence, and finite-sample error. In reinforcement learning, we analyze kernel-based Q-learning and derive finite-sample complexity bounds for learning an ϵ-optimal policy in large state–action spaces, where the efficiency is characterized by the kernel’s information gain. Together, these results provide a unified sample-complexity perspective on kernel methods across different learning settings, with brief remarks on related work in topological data analysis and signal processing.