Fair Regression under Sample Selection Bias

Wei Du, Xintao Wu, Hanghang Tong

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Recent research on fair regression focused on developing new fairness notions and approximation methods as target variables and even the sensitive attribute are continuous in the regression setting. However, all previous fair regression research assumed the training data and testing data are drawn from the same distributions. This assumption is often violated in real world due to the sample selection bias between the training and testing data. In this paper, we develop a framework for fair regression under sample selection bias when dependent variable values of a set of samples from the training data are missing as a result of another hidden process. Our framework adopts the classic Heckman model for bias correction and the Lagrange duality to achieve fairness in regression based on a variety of fairness notions. Heckman model describes the sample selection process and uses a derived variable called the Inverse Mills Ratio (IMR) to correct sample selection bias. We use fairness inequality and equality constraints to describe a variety of fairness notions and apply the Lagrange duality theory to transform the primal problem into the dual convex optimization. For the two popular fairness notions, mean difference and mean squared error difference, we derive explicit formulas without iterative optimization, and for Pearson correlation, we derive its conditions of achieving strong duality. We conduct experiments on three real-world datasets and the experimental results demonstrate the approach's effectiveness in terms of both utility and fairness metrics.

Original languageEnglish (US)
Title of host publicationProceedings - 2022 IEEE International Conference on Big Data, Big Data 2022
EditorsShusaku Tsumoto, Yukio Ohsawa, Lei Chen, Dirk Van den Poel, Xiaohua Hu, Yoichi Motomura, Takuya Takagi, Lingfei Wu, Ying Xie, Akihiro Abe, Vijay Raghavan
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages10
ISBN (Electronic)9781665480451
StatePublished - 2022
Event2022 IEEE International Conference on Big Data, Big Data 2022 - Osaka, Japan
Duration: Dec 17 2022Dec 20 2022

Publication series

NameProceedings - 2022 IEEE International Conference on Big Data, Big Data 2022


Conference2022 IEEE International Conference on Big Data, Big Data 2022


  • algorithmic fairness
  • regression analysis
  • sample selection bias

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Networks and Communications
  • Information Systems
  • Information Systems and Management
  • Safety, Risk, Reliability and Quality
  • Control and Optimization


Dive into the research topics of 'Fair Regression under Sample Selection Bias'. Together they form a unique fingerprint.

Cite this