报告摘要：

Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces, where classical regression techniques that rely on vector space structure no longer apply. We introduce E2M (End-to-End Metric regression), a deep learning framework for predicting metric space-valued outputs. E2M performs prediction via weighted Fréchet means over training outputs, where the weights are learned by a neural network conditioned on the input. This construction provides a principled mechanism for geometry-aware prediction that avoids surrogate embeddings and restrictive parametric assumptions, while fully preserving the intrinsic geometry of the output space. We establish theoretical guarantees, including a universal approximation theorem that characterizes the expressive capacity of the model and a convergence analysis of the entropy-regularized training objective. Through extensive simulations involving probability distributions, networks, and symmetric positive-definite matrices, we show that E2M consistently achieves state-of-the-art performance, with its advantages becoming more pronounced at larger sample sizes. Applications to human mortality distributions and New York City taxi networks further demonstrate the flexibility and practical utility of this framework.

报告人简介：

周易东博士现为加州大学戴维斯分校统计系博士后研究员，师从国际著名统计学家 Hans-Georg Müller 教授，即将于2026年秋季加入明尼苏达大学统计糖心视频 担任助理教授。他于中国科学技术大学获得学士学位，加州大学戴维斯分校获得统计学博士学位。其研究聚焦于统计理论、机器学习与几何数据分析的交叉领域，主要包括 Fréchet 回归、因果推断、深度学习以及非欧几里得数据分析等方向。研究成果发表于 JASA、JMLR、JRSS-B、JCGS和Biometrics 等国际顶级期刊，并有多篇工作被 NeurIPS、ICML 等机器学习顶级会议录用。