主题：A Framework for Statistical Inference via Randomized Algorithms
主讲人：张志翔 澳门大学
主持人：刘一鸣 威尼斯欢迎你welcome
时间：2024年9月25日（周三）上午11:00-12:00
地点：威尼斯欢迎你welcome石牌校区教学大楼115室
摘要
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs, leading to the problem of evaluating their accuracy. In this paper, we develop a statistical inference framework for quantifying the uncertainty of the outputs of randomized algorithms. We develop appropriate statistical methods---sub-randomization, multi-run plug-in and multi-run aggregation inference---by using multiple runs of the same randomized algorithm, or by estimating the unknown parameters of the limiting distribution. As examples, we develop methods for statistical inference for least squares parameters via random sketching. We characterize their limiting distribution via sketch-and-solve as well as partial sketching methods considering both the fixed and growing dimensional cases. The inference framework can also be applied to stochastic approximation, such as stochastic gradient descent. The results are supported via a broad range of simulations.
主讲人简介
Zhixiang Zhang is currently an Assistant Professor in the Department of Mathematics at the University of Macau. Previously, he completed his Ph.D. in Statistics at Nanyang Technological University and was a postdoctoral researcher in the Department of Statistics and Data Science at the University of Pennsylvania. His research interests lie in random matrix theory, high-dimensional statistics, and statistical machine learning. He has published works in the Annals of Statistics, Bernoulli, and IEEE Transactions on Information Theory.
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校对|刘一鸣
责编| 彭 毅
初审| 姜云卢
终审发布| 何凌云
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