How does promoting the minority fraction affect generalization? A theoretical study of one-hidden-layer neural network on group imbalance

Hongkang Li, Shuai Zhang, Yihua Zhang, Meng Wang, Sijia Liu, Pin Yu Chen

Research output: Contribution to journalArticlepeer-review

Abstract

Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high <italic>average</italic> accuracy is accompanied by low accuracy in a <italic>minority</italic> group. Despite algorithmic efforts to improve the minority group accuracy, a theoretical generalization analysis of ERM on individual groups remains elusive. By formulating the group imbalance problem with the Gaussian Mixture Model, this paper quantifies the impact of individual groups on the sample complexity, the convergence rate, and the average and group-level testing performance. Although our theoretical framework is centered on binary classification using a one-hidden-layer neural network, to the best of our knowledge, we provide the first theoretical analysis of the group-level generalization of ERM in addition to the commonly studied average generalization performance. Sample insights of our theoretical results include that when all group-level co-variance is in the medium regime and all mean are close to zero, the learning performance is most desirable in the sense of a small sample complexity, a fast training rate, and a high average and group-level testing accuracy. Moreover, we show that increasing the fraction of the minority group in the training data does not necessarily improve the generalization performance of the minority group. Our theoretical results are validated on both synthetic and empirical datasets, such as CelebA and CIFAR-10 in image classification.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalIEEE Journal on Selected Topics in Signal Processing
DOIs
StateAccepted/In press - 2024

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Biological neural networks
  • Classification algorithms
  • Complexity theory
  • Data models
  • Explainable machine learning
  • Gaussian mixture model
  • generalization analysis
  • group imbalance
  • Neural networks
  • Neurons
  • Training

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