Department of Industrial Engineering & Decision Analysis  - On Excess Risk Convergence Rates of Neural Network Classifiers

10:30am - 12:00pm
Room 2302 (lift 17-18)

We study the binary classification of unbounded data from R^d generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks. We obtain – for the first time – non-asymptotic upper bounds and convergence rates of the excess risk (excess misclassification error) for the classification without restrictions on model parameters. The convergence rates we derive do not depend on dimension d, demonstrating that deep ReLU networks can overcome the curse of dimensionality in classification. While the majority of existing generalization analysis of classification algorithms relies on a bounded domain, we consider an unbounded domain by leveraging the analyticity and fast decay of Gaussian distributions. To facilitate our analysis, we give a novel approximation error bound for general analytic functions using ReLU networks, which may be of independent interest. Gaussian distributions can be adopted nicely to model data arising in applications, e.g., speeches, images, and texts; our results provide a theoretical verification of the observed efficiency of deep neural networks in practical classification problems. This talk will base on https://arxiv.org/abs/2308.08030.

講者/ 表演者:
Prof. Xiaoming HUO
School of Industrial and Systems Engineering, Georgia Institute of Technology

Xiaoming Huo is A. Russell Chandler III Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech and Associate Director for Research at the Institute for Data Science and Engineering. Dr. Huo is also an associate director in the Master of Science in Analytics program. Dr. Huo's research interests include statistical theory and computing, optimization, and data sciences. His papers appeared in top journals, and some of them are highly cited. He is a senior member of IEEE and a Fellow of ASA. He was the sole winner of the Georgia Tech Sigma Xi Young Faculty Award in 2005. His work led to an interview by Emerging Research Fronts in June 2006 in the field of Mathematics -- every two months, one paper is selected. Dr. Huo received a Ph.D. degree in statistics from Stanford University, Stanford, CA, in 1999. He participated in the 30th International Mathematical Olympiad (IMO), held in Braunschweig, Germany, 1989 and received a gold prize.

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