Boedihardjo March, Strohmer Thomas, Vershynin Roman
Department of Mathematics, Michigan State University, East Lansing, USA.
Department of Mathematics, University of California, Davis, USA.
Proc Am Math Soc. 2025 Feb;153(2):773-782. doi: 10.1090/proc/17126. Epub 2025 Jan 8.
We show how randomized rounding based on Grothendieck's identity can be used to prove a nearly tight bound on the covariance loss-the amount of covariance that is lost by taking conditional expectation. This result yields a new type of weak Szemeredi regularity lemma for positive semidefinite matrices and kernels. Moreover, it can be used to construct differentially private synthetic data.
我们展示了如何基于格罗滕迪克恒等式的随机舍入来证明协方差损失的一个近乎紧的界——通过取条件期望而损失的协方差量。该结果为半正定矩阵和核产生了一种新型的弱塞梅雷迪正则性引理。此外，它可用于构造差分隐私合成数据。
