题目：Statistical Inference of GLMs and Causal Effects in Observational Studies under Proportional Asymptotics

报告人：刘林 副教授 (上海交通大学)

地点: 致远楼108室

时间: 2024年10月10日 15:30-17:00

报告人简介：刘林于2011年同济大学生命科学学院本科毕业，专业生物信息，于2018年取得哈佛大学生物统计博士，2020年底入职上海交通大学自然科学研究院，任职长聘教轨副教授。目前研究方向为因果推断、非参数/半参数统计理论、机器学习理论、及统计学在生物医学中的应用。

Abstract：In this talk, we consider the statistical problem that even undergraduates know about -- inference on regression coefficients in GLMs. This problem is almost completely addressed in the low-dimensional setting ($p \ll \sqrt{n}$) and in the traditional high-dimensional sparse setting ($p \gg n$ but $s \ll n$). Here, we consider the ``modern'' high-dimensional setting with $p / n \rightarrow c \in (0, \infty)$. We first survey the current state-of-the-art methods based on mainly Approximate Message Passing (AMP) and Stein's lemma under Gaussian designs. AMP-based construction is well-known to be difficult to understand for statisticians who have no background in statistical physics. Interestingly, we show that, despite the success of AMP, we can instead construct extremely simple, moment-based estimators that have almost the same theoretical and empirical guarantees as the AMP-based estimators. These estimators do not require any AMP machinary and can be easily generalized to non-Gaussian settings. Numerical experiments support our theoretical findings. Finally, if time permitting, we will discuss how the moment approach can also boost (1) AMP-based estimators and (2) recent proposals by statistical physicists on empirical Bayes methods for high-dimensional GLMs.

欢迎各位参加！