Proposer of the vote of thanks to Whiteley et al. and contribution to the Discussion of ‘Statistical exploration of the Manifold Hypothesis’
本文回应Whiteley等人的工作，提出潜度量模型（LMM）从统计依赖角度解释低维几何结构如何自然产生，为流形假设提供概率基础，对高维数据分析者有用。
Whiteley et al. revisit one of the most influential ideas in modern statistical learning: the manifold hypothesis. While the hypothesis is routinely invoked to justify the success of high-dimensional data analysis, it is rarely given a probabilistic explanation. The central contribution of this paper is to show how low-dimensional geometric structure can emerge naturally from statistical dependence among random coordinate functions, rather than being imposed a priori. The proposed Latent Metric Model (LMM) provides a mathematically coherent framework linking latent structure, kernel geometry, and observed data geometry. In this sense, the paper offers not merely a reformulation of the manifold hypothesis, but a principled explanation for why manifold-like data structures may arise in practice.