报告题目：Tuning-free Estimation and Inference of Cumulative Distribution Function under Local Differential Privacy

报告人：Linglong Kong教授 - 加拿大阿尔伯塔大学

邀请人：徐晨 教授

报告时间：2025 年3月31日 10：00 - 11：00

报告地点： 兴庆校区数学楼2-3会议室

报告摘要：

We introduce a novel algorithm for estimating Cumulative Distribution Function (CDF) values under Local Differential Privacy (LDP) by exploiting an unexpected connection between LDP and the current status problem, a classical survival data problem in statistics. This connection leads to the development of tools for constrained isotonic estimation based on binary queries. Through mathematical proofs and extensive numerical testing, we demonstrate that our method achieves uniform and L2 error bounds when estimating the entire CDF curve. By employing increasingly dense grids, the error bound can be improved, exhibiting an asymptotic normal distribution of the proposed estimator. Theoretically, we show that the error bound smoothly changes as the number of grids increases relative to the sample size n. Computationally, we demonstrate that our constrained isotonic estimator can be efficiently computed deterministically, eliminating the need for hyperparameters or random optimization.

报告人简介：

Dr. Linglong Kong (孔令龙)，加拿大阿尔伯塔大学数学与统计系教授、加拿大首席科学家及加拿大高等研究院AI 领域特聘专家。他入选American Statistical Association和 Alberta Machine Intelligence Institute的会士, 现任统计学权威期刊JASA、 AoAS、 CJS、 STAT INTERFACE 的副主编，在统计学及机器学习顶刊、顶会发表学术论文120余篇，产生了广泛的学术影响力。他的研究兴趣包括高维统计、神经图像处理、稳健统计方法、分位数回归及智能健康等领域。