用赫林格距离改进GAN训练，提升稳定性和抗干扰能力
Hellinger loss function for Generative Adversarial Networks
- 基于赫林格距离设计新型对抗损失函数，兼具对称性与鲁棒性
- 理论证明参数估计存在唯一且渐近正态，联合估计更稳定
- 实测在污染数据下表现优于传统GAN，尤其在噪声干扰时更鲁棒
我们提出用于生成对抗网络（GAN）训练的赫林格型损失函数，其设计灵感来自赫林格距离的有界性、对称性和鲁棒性。定义基于该散度的对抗目标，并在一般参数框架下研究其统计性质。证明了由对抗训练得到的估计量存在、唯一、一致，并具有联合渐近正态性。特别地，分析了生成器与判别器参数的联合估计，提供了完整的渐近刻画。引入两种赫林格型损失的实现方式，并在控制模拟实验中评估其性能，相较于经典的（最大似然型）GAN损失，两者均在数据污染程度增加时表现出更高的估计精度和鲁棒性。
原文摘要 · Abstract (English)
We propose Hellinger-type loss functions for training Generative Adversarial Networks (GANs), motivated by the boundedness, symmetry, and robustness properties of the Hellinger distance. We define an adversarial objective based on this divergence and study its statistical properties within a general parametric framework. We establish the existence, uniqueness, consistency, and joint asymptotic normality of the estimators obtained from the adversarial training procedure. In particular, we analyze the joint estimation of both generator and discriminator parameters, offering a comprehensive asymptotic characterization of the resulting estimators. We introduce two implementations of the Hellinger-type loss and we evaluate their empirical behavior in comparison with the classic (Maximum Likelihood-type) GAN loss. Through a controlled simulation study, we demonstrate that both proposed losses yield improved estimation accuracy and robustness under increasing levels of data contamination.
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