报告题目1：On Ratio-Based Loss Functions

报告人：Professor Andreas Christmann，University of Bayreuth, Germany

报告时间：2026年5月18日（周一）14:30-17:30

报告地点：20-200

报告摘要：Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and (iii) the set of probability measures, which are allowed for the specified algorithm. This talk gives a survey of a certain class of loss functions, which we call ratio-based. In supervised learning, margin-based loss functions for classification problems depending on the product of the output values and the predictions as well as distance-based loss functions depending on the difference of the output values and the predictions for regression or quantile regression are common. Distance-based loss functions are in particular useful, if an additive model assumption seems plausible, i.e. under the common signal plus noise assumption. However, several loss functions proposed in the literature for regression purposes have a multiplicative error structure in mind and pay attention to relative errors, i.e. to the ratio of the output values and the predictions, where sometimes a link function is involved. In this talk, such ratio-based loss functions will be systematically investigated from a general point of view and a few new losses, which may be of interest, will be introduced. The talk does not focus on a specific machine learning algorithm. Instead, we hope that this talk can stimulate some interest in the class of ratio-based loss functions to encourage future research on various ML algorithms. This is joint work with my PhD student Lena Helgerth.

报告人简介：Andreas Christmann received a Ph.D degree from University of Dortmund, Germany. After positions as professor at KUL in Leuven and at VUB in Brussels (both in Belgium), he is a Full Professor and Chair for Stochastics and Machine Learning in the Department of Mathematics, University of Bayreuth, Germany. His research interests include statistical learning theory, kernel methods, robust statistics, and statistical methods for big data. He has published many research papers and 1 monograph entitled “Support Vector Machine”in these areas. He is an Action Editor for “Journal ofMachine Learning Research”from 2013 to 2019.Since 2020, he is the member of the JMLR Editorial board of reviewers.

报告题目2：Stochastic Gradient Methods: Bias, Stability and Generalization

报告人：雷云文，香港大学

报告时间：2026年5月18日（周一）14:30-17:30

报告地点：20-200

报告摘要：Recent developments of stochastic optimization often suggest biased gradient estimators to improve either the robustness, communication efficiency or computational speed. Representative biased stochastic gradient methods (BSGMs) include Zeroth-order stochastic gradient descent (SGD), Clipped-SGD and SGD with delayed gradients. In this talk, we present the first framework to study the stability and generalization of BSGMs for convex and smooth problems. We apply our general result to develop the first stability bound for Zeroth-order SGD with reasonable step size sequences, and the first stability bound for Clipped-SGD. While our stability analysis is developed for general BSGMs, the resulting stability bounds for both Zeroth-order SGD and Clipped-SGD match those of SGD under appropriate smoothing/clipping parameters.

报告人简介：雷云文，于武汉大学获得博士学位，现为香港大学数学系副教授，其研究方向包括机器学习、数据科学、学习理论与随机优化。同时，他担任Machine Learning, Transactions on Machine Learning Research, IEEE Transactions on Neural Networks and Learning Systems副编辑，并兼任国际机器学习大会（ICML）、神经信息处理系统大会（NeurIPS）、国际学习表征会议（ICLR）及国际人工智能与统计会议（AISTATS）的领域主席。

邀请人：向道红