| Abstract |
The field exploring the interplay between statistics and geometry has been expanding rapidly in both scope and influence. The idea of manifold fitting traces back to H. Whitney’s work in the early 1930s. A central question is: given a set of data, under what conditions can we find a smooth d-dimensional surface (or manifold) that approximates it well, and how can we quantify the quality of that fit in terms of distance and smoothness?
In this talk, I will give an overview of the manifold fitting problem and highlight some recent insights and developments. I will focus on applications in NMR-based metabolomics—where manifold fitting helps reveal metabolic variation in the UK Biobank population—and in single-cell RNA analysis. The discussion will draw on recent work by Yao, Yau, and collaborators, as well as ongoing research. |
