Topic: Machine Learning in Banach Spaces: A Black-box or White-box Method?

Speaker: Prof. Qi Ye, South China Normal University

Time: 10:00-12:00, July 15th, 2022

Tencent meeting ID: 659- 977- 944

Organizor: School of Mathematics and Statistics, HENU

Report summary: In this lecture, we will deal with the whole theory of regularized learning for generalized data in Banach spaces including representer theorems, approximation theorems, and convergence theorems. Specially, we combine the data-driven and model-driven methods to study the new algorithms and theorems of regularized learning. Usually, the data-driven and model-driven methods are used to analyze the black-box and white-box models, respectively. With the same thought as the Tai Chi diagram, we use the discrete local information of the black-box and white-box models to construct the global approximate solutions by regularized learning. Our original ideas are inspired by eastern philosophy such as the golden mean. The work of the regularized learning for generalized data provides another road to study the algorithms of machine learning from three aspects: 1)the interpretability in approximation theory;2)the nonconvexity and nonsmoothness in optimization theory;3)the generalization and overfitting in regularization theory. Moreover, based on the theory of regularized learning, we will construct the composite algorithms combining support vector machines, artificial neural networks, and decision trees for our current research projects on big data analytics in education and medicine.

Profile: Qi Ye is a professor and doctoral supervisor at South China Normal University School of Mathematical Sciences, China. He is engaged in the theory and application of kernel function approximation methods.