Speaker: 宁建辉，华中师范大学

Inviter: 熊世峰

Title: Projected Representative Points: Enhancing Representativeness in Projection Spaces

Language: Chinese

Time & Venue: 2025.11.29 15:30-16:00 腾讯会议：979-347-585

Abstract: Representative points are a widely used method for statistical inference and subdata selection. In the literature, numerous methods have been proposed to obtain representative points efficiently. These include mean square error representative points, F -discrepancy representative points, kernel herding, principal points, support points, and so on. These methods are based on different criteria, but the basic idea of these criteria is the same: measuring the deviation between the empirical distribution and the overall distribution. A common shortcoming of these methods is their failure to consider the representativeness of the representative points in the low-dimensional projection space. This may not be a significant issue in low-dimensional problems, it can have severe consequences in high-dimensional scenarios. In this paper, we present a novel approach, the projected representative point method, which addresses this limitation by leveraging the kernel discrepancy and the Bayesian weighted kernel. Additionally, we provide a detailed description of the construction algorithm for this method. To illustrate the efficacy of the projected representative points, we provide several numerical examples.