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.