[演講公告] Sample Complexity of Kernel Methods for Machine Learning
發布日期： 2025-12-17 公告單位： 數學系
主 講 人：葉行遠博士 (國立臺灣大學資料科學學位學程)
演講題目：Sample Complexity of Kernel Methods for Machine Learning
演講時間：2025年12月22日(星期一) 15:30 ~ 17:00
演講地點：中央大學鴻經館M107
Abstract：
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.
演講題目：Sample Complexity of Kernel Methods for Machine Learning
演講時間：2025年12月22日(星期一) 15:30 ~ 17:00
演講地點：中央大學鴻經館M107
Abstract：
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.
更新日期: 2025-12-17
公告類別: 演講
瀏覽人次: 103