报告题目：Environment Invariant Generalized Linear Model: Theory and Algorithm
报告人：孔令臣（教授博导），北京交通大学（北京）
报告时间：9月28日（周一）8:30-10:00
报告地点：思学楼C110
报告人简介：
孔令臣，北京交通大学数学与统计学院教授、博士生导师，担任中国运筹学会数学规划分会理事长、组织委员会副主任。研究工作涵盖对称锥互补与最优化、高维数据分析、统计优化与学习及其应用。已在 Mathematical Programming、SIAM Journal on Optimization、IEEE Transactions on Pattern Analysis and Machine Intelligence、Technometrics、Statistica Sinica 等期刊发表论文100余篇，主持国家重点研发计划、国家自然科学基金重点项目及面上项目等10余项。曾获2012年中国运筹学会青年奖、2018年北京市高等教育教学成果一等奖，以及2022年教育部自然科学二等奖、北京市高等教育教学成果二等奖。
报告内容摘要：
Learning invariant predictive relationships across heterogeneous environments is crucial for out-of-distribution (OOD) generalization and stable feature identification. In this work, we study a sparse environment-invariant generalized linear model (EIGLM) and formulate its estimator with an explicit sparsity constraint. From a statistical perspective, we establish that the population objective uniquely identifies the true invariant parameter, and we derive non-asymptotic estimation error bounds together with support recovery consistency guarantees in high-dimensional regimes. From a computational perspective, we reformulate the estimator as a sparsity-constrained binary integer program and introduce a sharp-peak penalty function. We prove an exact penalty theorem, demonstrating that the penalized formulation is equivalent to the original mixed-integer model beyond a solution-independent threshold; furthermore, we characterize first-order optimality via P-stationarity. We then develop an alternating proximal gradient descent algorithm with closed-form proximal updates, establishing subsequence convergence, finite-step binary identification, global sequence convergence, and linear convergence rates under mild assumptions. Extensive numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed method in identifying invariant and causal variables while maintaining competitive predictive accuracy.
主办单位：理学院、人工智能研究院
科学技术发展研究院
