Adaptive Estimation of Nonparametric Functionals

主讲人：刘林  上海交通大学教授

时间：2021年6月2日15：00

地点：三号楼332室

举办单位：数理学院

主讲人介绍：Lin Liu is an Assistant Professor at the Institute of Natural Sciences, School  of Mathematical Sciences and Center for Biostatistics at Shanghai Jiao Tong  University. He obtained his PhD from the Department of Biostatistics at Harvard  University. Before that, he studied bioinformatics at Tongji University. His  current research interest includes mathematical statistics, causal inference,  optimal sequential decision making and theoretical machine learning.

内容介绍：Estimating regression and probability density functions is the main focus in  machine learning and AI. However, functional estimation is the center pillar in  statistics. In this talk, I provide general adaptive (aka, data-driven) upper  bounds for estimating nonparametric functionals based on second-order  U-statistics arising from finite-dimensional approximation of the  infinite-dimensional models, based on the celebrated Lepskii's method. I will  provide examples of functionals for which the theory produces rate optimally  matching adaptive upper and lower bounds and these examples have potential  application value in machine learning and AI. Our results are  information-theoretically optimal and the first of such in statistics. At the  end of my talk, I will also discuss some partial results related to optimal  adaptive uncertainty quantification for functionals and several related open  problems: e.g. how to generalize our theory to functionals of the solution to  inverse problems and when deep learning could be provably optimal for functional  estimation.