Seminar 2023-10-20

Functional Data Analysis Through the Lens of Deep Neural Networks

Guanqun Cao

Associate Professor

Department of Computational Mathematics, Science, and Engineering

Michigan State University

Date: Friday, October 20, 2023

Time: 11:00 A.M. – 12:00 P.M. Eastern Time

Location: Johnson Center, Room 325 Meeting Room A

Functional data refer to curves or functions, i.e., the data for each variable are viewed as smooth curves, surfaces, or hypersurfaces evaluated at a finite subset of some interval in 1D, 2D, and 3D. Advancements in modern technology have enabled the collection of sophisticated, ultra high-dimensional datasets, thus boosting the investigation of functional data. In this talk, I will first introduce a deep neural networks-based robust method to perform nonparametric regression for multi-dimensional functional data. The proposed estimators are based on sparsely connected deep neural networks with rectifier linear unit activation function. Meanwhile, the estimators are less susceptible to outlying observations and model-misspecification. For any multi-dimensional functional data, we provide uniform convergence rates for the proposed robust deep neural networks estimators. Then, I will present a new approach, called functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principal components of the training data which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches which only work for one-dimensional functional data, the proposed FDNN approach applies to general non-Gaussian multi-dimensional functional data.

Dr. Guanqun Cao is an Associate Professor of the Departments of Statistics and Probability and Department of Computational Mathematics, Science and Engineering at Michigan State University. Prior to joining Michigan State University in 2023, she was a faculty member of Auburn University. She obtained her Ph.D. in Statistics from the Department of Statistics and Probability at Michigan State University. Working at the interface of statistics, mathematics, and computer science, Dr. Cao is interested in developing cutting-edge statistical methods for solving issues related to data science and big data analytics. The methods she developed have a wide application in engineering, neuroimaging, environmental studies, and biomedical science. Dr. Cao is an Elected Member of the International Statistical Institute.

Nicholas Rios

David Kepplinger