A Framework for Statistical Inference Via Randomized Algorithms

发布时间：2024-06-28 作者：浏览次数：

Speaker:	张志翔	DateTime:	2024年6月29日（周六）上午10：30-11：30
Brief Introduction to Speaker: 张志翔，澳门大学助理教授，2016年在中国科学技术大学获得学士学位。2021年在南洋理工大学获得统计学博士学位。宾夕法尼亚大学沃顿商学院统计与数据科学系的博士后研究员。主要方向高维统计学，随机矩阵理论，统计学机器学习。		Place:	六号楼6401
Abstract:Randomized algorithms, such as randomized sketching or projections, 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 an example, we develop methods for statistical inference for least squares parameters via random sketching using matrices with i.i.d. entries, or uniform partial orthogonal matrices. For this, we characterize the limiting distribution of estimators obtained via sketch-and-solve as well as partial sketching methods. The analysis of i.i...