Minimax Regret Learning for Data with Heterogeneous Subgroups
arxiv(2024)
摘要
Modern complex datasets often consist of various sub-populations. To develop
robust and generalizable methods in the presence of sub-population
heterogeneity, it is important to guarantee a uniform learning performance
instead of an average one. In many applications, prior information is often
available on which sub-population or group the data points belong to. Given the
observed groups of data, we develop a min-max-regret (MMR) learning framework
for general supervised learning, which targets to minimize the worst-group
regret. Motivated from the regret-based decision theoretic framework, the
proposed MMR is distinguished from the value-based or risk-based robust
learning methods in the existing literature. The regret criterion features
several robustness and invariance properties simultaneously. In terms of
generalizability, we develop the theoretical guarantee for the worst-case
regret over a super-population of the meta data, which incorporates the
observed sub-populations, their mixtures, as well as other unseen
sub-populations that could be approximated by the observed ones. We demonstrate
the effectiveness of our method through extensive simulation studies and an
application to kidney transplantation data from hundreds of transplant centers.
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