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A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization
Renzhe Xu · Peng Cui · Zheyan Shen · Xingxuan Zhang · Tong Zhang

Covariate-shift generalization, a typical case in out-of-distribution (OOD) generalization, requires a good performance on the unknown testing distribution, which varies from the accessible training distribution in the form of covariate shift. Recently, independence-driven importance weighting algorithms have shown empirical effectiveness to deal with covariate-shift generalization on several learning models, including regression algorithms and deep neural networks, while their theoretical analyses are missing. In this paper, we theoretically prove the effectiveness of such algorithms by explaining them as feature selection processes. We first specify a set of variables, named minimal stable variable set, that is minimal and optimal to deal with covariate-shift generalization for common loss functions, such as the mean squared loss and binary cross-entropy loss. Afterward, we prove that under ideal conditions, independence-driven importance weighting algorithms could identify the variables in this set. Analysis of asymptotic properties is also provided. These theories are further validated in several synthetic experiments.

Author Information

Renzhe Xu (Tsinghua University)
Peng Cui (Tsinghua University)
Peng Cui

Peng Cui is an Associate Professor in Tsinghua University. He got his PhD degree from Tsinghua University in 2010. His research interests include causal inference and stable learning, network representation learning, and human behavioral modeling. He has published more than 100 papers in prestigious conferences and journals in data mining and multimedia. His recent research won the IEEE Multimedia Best Department Paper Award, SIGKDD 2016 Best Paper Finalist, ICDM 2015 Best Student Paper Award, SIGKDD 2014 Best Paper Finalist, IEEE ICME 2014 Best Paper Award, ACM MM12 Grand Challenge Multimodal Award, and MMM13 Best Paper Award. He is the Associate Editors of IEEE TKDE, IEEE TBD, ACM TIST, and ACM TOMM etc. He has served as program co-chair and area chair of several major machine learning and artificial intelligence conferences, such as IJCAI, AAAI, ACM CIKM, ACM Multimedia etc.

Zheyan Shen (Tsinghua University)
Xingxuan Zhang (Tsinghua University)
Tong Zhang (HKUST)
Tong Zhang

Tong Zhang is a professor of Computer Science and Mathematics at the Hong Kong University of Science and Technology. His research interests are machine learning, big data and their applications. He obtained a BA in Mathematics and Computer Science from Cornell University, and a PhD in Computer Science from Stanford University. Before joining HKUST, Tong Zhang was a professor at Rutgers University, and worked previously at IBM, Yahoo as research scientists, Baidu as the director of Big Data Lab, and Tencent as the founding director of AI Lab. Tong Zhang was an ASA fellow and IMS fellow, and has served as the chair or area-chair in major machine learning conferences such as NIPS, ICML, and COLT, and has served as associate editors in top machine learning journals such as PAMI, JMLR, and Machine Learning Journal.

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