Maozai Tian, Shaopei Ma, Zhen Yu, and Yanan Hu’s contribution to the Discussion of ‘Statistical exploration of the manifold hypothesis’ by Whiteley et al.
Abstract
We want to congratulate the authors on the publication of ‘Statistical Exploration of the Manifold Hypothesis’ in JRSS-B. They proposed the Latent Metric Space model, which produces a hidden, low-dimensional manifold structure in high-dimensional data, thus providing a statistical justification for the manifold hypothesis. This article is an insightful and highly stimulating work. Here are several comments and suggestions. Consider the Latent Metric Space model: For the LMS model, the main focus is on the following issues: For each p≥1, the rank r of the mean correlation kernel f is finite, and r and 1/λrf are bounded as p→∞. How to choose the optimal r? supj≥1supz∈ZE[|Xj(z)|4]
Fields of Study & Subjects
Statistical Methods and Applications
Topological and Geometric Data Analysis
Face and Expression Recognition
Publication details
- Journal / source
- Journal of the Royal Statistical Society Series B (Statistical Methodology)
- Volume
- 88
- Issue
- 2
- Pages
- 426–430
- Publication date
- 8 January 2026
- Language
- EN