The challenge of developing accurate regression models from limited data samples remains one of the most persistent obstacles in contemporary machine learning research and industrial applications. Small-sample regression problems arise across diverse domains, including materials science, chemical process engineering, biomedical research, and manufacturing quality control, where data acquisition is inherently expensive, time-consuming, or physically constrained. This comprehensive review examines the transformative role of Generative Adversarial Networks (GANs) in addressing small-sample regression challenges through synthetic data augmentation and intelligent model fitting strategies. The review systematically analyses the theoretical foundations of GAN architectures, beginning with the seminal work on adversarial training frameworks and progressing through significant variants including Wasserstein GANs, conditional GANs, and their hybrid formulations specifically designed for regression tasks. Particular attention is devoted to virtual sample generation methodologies that leverage GAN-based approaches to expand limited training datasets whilst preserving the underlying data distribution characteristics and feature correlations essential for accurate regression modelling. The review further explores intelligent fitting techniques that integrate GAN-generated samples with conventional machine learning algorithms, examining how these combined approaches enhance prediction accuracy, model generalisation, and robustness in data-scarce scenarios. Critical evaluation of training stability issues, including mode collapse and convergence challenges specific to regression applications, is presented alongside established mitigation strategies. Comparative analysis with alternative generative models, particularly Variational Autoencoders and emerging diffusion models, provides practitioners with guidance for method selection. The review concludes by identifying current limitations, highlighting promising research directions, and offering practical recommendations for implementing GAN-based augmentation strategies in real-world small-sample regression applications.
Chongyuan Jiao (Wed,) studied this question.