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

报告人：叶颀

单   位：华南师范大学

时   间：7月15日10:00

地   点：腾讯659 977 944

摘要：In this talk, we study 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 the 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 of 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 the regularized learning. Our original ideas are inspired by the 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 including: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 the regularized learning, we will construct the composite algorithms combining support vector machines, artificial neural networks, and decision trees for our current research projects of the big data analytics in education and medicine.

报告人简介：叶颀,华南师范大学数学科学学院教授和博士生导师，一直从事核函数逼近方法的理论及其应用研究。叶教授博士师从于美国伊利诺理工大学的核函数逼近方法专家Gregory E. Fasshauer教授，随后到美国雪城大学与计算数学专家许跃生教授展开博士后研究工作，之后又到香港与径向基函数专家韩耀宗教授和凌立云教授展开合作研究。叶教授是第十二批国家海外高层次人才引进计划青年项目入选者，目前主持自科基金面上项目1项和参与自科基金重点项目1项, 并是自科基金数学天元基金“数学与医疗健康交叉重点专项”的项目负责人。叶教授主要研究逼近论及其在机器学习与数据分析中的应用，并和许跃生教授共同提出了国际原创性研究课题——稀疏机器学习方法，论文《Generalized Mercer Kernels and Reproducing Kernel Banach Spaces》发表在美国数学学会期刊《Memoirs of the American Mathematical Society》（该期刊每期只刊登一篇文章），并是该期刊发表的首篇关于机器学习的论文，也是国内计算数学工作者首次在该期刊发表的长文。叶教授在华南师范大学采用“抽象理论、具体算法、落地应用”三位一体的科研新模式，联合国内外专家学者成立了“机器学习与最优化计算实验室”，以机器学习方法的数学理论为主要研究目标，研究范畴包括逼近论、最优化理论、支持向量机、人工神经网络、医学图像处理和癌症演化建模等，并将相关研究成果应用于医疗和教育大数据分析，开发具有自主知识产权的医疗和教育辅助软件。