统计与数据科学系系列学术报告之四百二十期

时间：2024年3月8日（周五）15:00-16:00

地点：史带楼601室

主持人：复旦大学管理学院统计与数据科学系朱仲义教授

报告人：冯兴东教授上海财经大学统计与管理学院

题目：Deep Nonparametric Quantile Regression under Covariate Shift

摘要：This work focuses on addressing the challenges posed by covariate shift in nonparametric quantile regression using deep neural networks. We propose a two-stage pre-training reweighted method that leverages importance weighting to mitigate the effects of distribution shift. In the first stage, density ratios are estimated through least-squares density ratio fitting. In the second stage, a deep neural network estimator is trained using pre-training weights. Theoretical analysis is provided, offering non-asymptotic error bounds for the deep estimators, including unweighted, reweighted, and pre-training reweighted estimators. We consider scenarios with both bounded and unbounded density ratios. Notably, we employ a novel proof technique to bound the generalization error, characterized by the size and weights bound of ReLU neural networks. This enables us to establish fast rates of convergence under the adaptive self-calibration condition, distinguishing our approach from those relying on local Rademacher complexity techniques. Additionally, we derive the approximation error with weight bounds for ReLU neural networks approximating the H\"older class. Our theoretical findings provide valuable insights for the pre-training process and highlight the efficacy of reweighted techniques. Numerical experiments are conducted to further validate the theoretical findings and demonstrate the effectiveness of our proposed method.

个人简介：冯兴东，博士毕业于美国伊利诺伊大学香槟分校，现任上海财经大学统计与管理学院院长、统计学教授、博士生导师。研究领域为数据降维、稳健方法、分位数回归以及在经济问题中的应用、大数据统计计算、强化学习等，在国际顶级统计学/计量经济学期刊JASA、AoS、JRSSB、Biometrika、JoE以及人工智能期刊/顶会JMLR、NeurIPS上发表论文多篇。2018年入选国际统计学会推选会员(Elected member)，2019年担任全国统计教材编审委员会第七届委员会专业委员（数据科学与大数据应用组），2020年担任第八届国务院学科评议组（统计学）成员，2022年担任全国应用统计专业硕士教指委委员，2023年担任全国工业统计学教学研究会副会长以及中国数学会概率统计分会常务理事，2022年起兼任国际统计学权威期刊Annals of Applied Statistics和Statistica Sinica编委（Associate Editor）以及国内统计学权威期刊《统计研究》编委。