Yao Zhigang 

National University of Singapore

Zhigang Yao is an Associate Professor in the Department of Statistics and Data Science at the National University of Singapore (NUS). He also holds a courtesy joint appointment with the Department of Mathematics at NUS. He is a Faculty Affiliate of the Institute of Data Science (IDS) at NUS. He received his Ph.D. in Statistics from University of Pittsburgh in 2011. His thesis advisors are Bill Eddy at Carnegie Mellon and Leon Gleser at University of Pittsburgh. He has been an Assistant Professor at NUS from 2014-2020. Before joining NUS, he has been working with Victor Panaretos as a post-doc researcher at the Swiss Federal Institute of Technology (EPFL) from 2011-2014.

From 2022, he has been a member of the Center of Mathematical Sciences and Applications (CMSA) at Harvard University. At Harvard, he collaborates with Shing-Tung Yau on manifold fitting and research the interface between statistics and geometry. He is also a Visiting Faculty in the Department of Statistics at Harvard. He is the organizer of the Harvard Conference on Geometry and Statistics, hosted by CMSA in 2023.

Abstract

Manifold fitting, which offers substantial potential for efficient and accurate modeling, poses a critical challenge in non-linear data analysis. This study presents a novel approach that employs neural networks to fit the latent manifold. Leveraging the generative adversarial framework, this method learns smooth mappings between low-dimensional latent space and high-dimensional ambient space, echoing the Riemannian exponential and logarithmic maps. The well-trained neural networks provide estimations for the latent manifold, facilitate data projection onto the manifold, and even generate data points that reside directly within the manifold. Through an extensive series of simulation studies and real data experiments, we demonstrate the effectiveness and accuracy of our approach in capturing the inherent structure of the underlying manifold within the ambient space data. Notably, our method exceeds the computational efficiency limitations of previous approaches and offers control over the dimensionality and smoothness of the resulting manifold. This advancement holds significant potential in the fields of statistics and computer science. The seamless integration of powerful neural network architectures with generative adversarial techniques unlocks new possibilities for manifold fitting, thereby enhancing data analysis. The implications of our findings span diverse applications, from dimensionality reduction and data visualization to generating authentic data. Collectively, our research paves the way for future advancements in non-linear data analysis and offers a beacon for subsequent scholarly pursuits. This talk is based on some results from the following references

https://www.pnas.org/doi/10.1073/pnas.2311436121 (Yao, Su and Yau, 2023),

https://arxiv.org/abs/2304.07680 (Yao, Su, Li and Yau, 2022)

https://arxiv.org/abs/1909.10228 (Yao and Xia, 2019).