報 告 人：胡慶培 研究員

報告題目：數據與機理結合的數據恢復與建模方法

報告時間：2023年12月7日（周四）下午14:30

報告地點：分析測試中心102會議室

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

       胡慶培，中國科學院數學與系統科學研究院研究員，現任系統所統計室主任、質量與數據科學中心常務副主任、航天產品可靠性技術與質量科學聯合實驗室副主任。長期從事工業統計與系統可靠性的研究工作，在系統可靠性綜合評估、加速退化試驗評估與設計、系統可靠性增長建模與推斷、復雜數據分析等方向研究成果發表于IISE、ITR、RESS、JQT、NeurIPS等，曾獲關肇直青年科學獎、IISE最佳年度論文提名獎等。目前擔任系統科學與數學、IISE、QTQM、QREI學術期刊的副編輯或編委。

報告摘要：

       Because of the widespread existence of noise and data corruption, recovering the true regression parameters with a certain proportion of corrupted response variables is an essential task. Methods to overcome this problem often involve robust least-squares regression, but few methods perform well when confronted with severeadaptive adversarial attacks. In many applications, prior knowledge is often available from historical data or engineering experience, and by incorporating prior information into a robust regression method, we develop an effective robust regression method that can resist adaptive adversarial attacks. First, we propose the novel TRIP (hard Thresholding approach to Robust regression with sImple Prior) algorithm, which improves the breakdown point when facing adaptive adversarial attacks. Then, to improve the robustness and reduce the estimation error caused by the inclusion of priors, we use the idea of Bayesian reweighting to construct the more robust BRHT (robust Bayesian Reweighting regression via Hard Thresholding) algorithm. We prove the theoretical convergence of the proposed algorithms under mild conditions, and extensive experiments show that under different types of dataset attacks, our algorithms outperform other benchmark ones. Finally, we apply our methods to a data-recovery problem in a real-world application involving a space solar array, demonstrating their good applicability.