Simon et al.’s contribution to the Discussion of ‘Statistical exploration of the Manifold Hypothesis’ by Whiteley et al.
Simon 等对《流形假说的统计探索》的讨论
We congratulate the authors on their impressive effort and commend their tour de force. Our comments follow below. Theoretical foundations. The authors contribution is driven by embedding the manifold hypothesis in a rigorous statistical framework. The Latent Manifold Model (LMM) plays a central role by integrating latent variables, random functions, and structured noise within a unified construction. Grounded in Mercer’s theorem, the approach links correlation kernels with…