A0693
Title: Projected representative points
Authors: Jianhui Ning - Central China Normal University (China) [presenting]
Abstract: Representative points play a pivotal role in statistical inference and optimal sub-data selection, with established methodologies including mean squared error (MSE) points, F-discrepancy representative points, kernel herding, principal points, and support points. These approaches, while diverse in formulation, share a common theoretical foundation: quantifying the divergence between empirical and target distributions. However, a critical limitation persists across these methods: Their inability to preserve representativeness in low-dimensional projection spaces. While this shortcoming is often negligible in low-dimensional settings, it can lead to significant information loss in high-dimensional applications. To address this challenge, the projected representative point (PRP) method is proposed, which integrates kernel discrepancy minimization with Bayesian-weighted kernel embeddings to ensure dimensional consistency. Through comprehensive numerical experiments, it is demonstrated that PRP achieves superior performance in preserving representation within low-dimensional projected space.
