论文标题
基于GAN的半监督学习如何工作？
How Does GAN-based Semi-supervised Learning Work?
论文作者
论文摘要
生成的对抗网络（GAN）已被广泛使用，并在半监督学习中取得了竞争成果。本文理论上分析了基于GAN的半监督学习（GAN-SSL）的工作方式。我们首先证明，鉴于固定的生成器，优化GAN-SSL的歧视器等同于优化监督学习的歧视器。因此，GAN-SSL中的最佳鉴别器预计在标记数据上是完美的。然后，如果完美的鉴别器可以进一步导致优化目标达到其理论最大值，则最佳发电机将匹配真实的数据分布。由于在实践中不可能达到理论上的最大值，因此人们不能期望获得生成数据的完美发生器，这显然与gan的目标不同。此外，如果标记的数据可以穿越数据歧管的所有连接子域，这在半监督分类中是合理的，我们还希望GAN-SSL中的最佳歧视器在未标记的数据上也是完美的。总之，GAN-SSL中的最小值优化理论上将通过意外地学习不完善的发电机，即GAN-SSL可以通过利用未标记的信息来有效地提高歧视者的普遍性，从而在标记和未标记数据上输出完美的歧视器。
Generative adversarial networks (GANs) have been widely used and have achieved competitive results in semi-supervised learning. This paper theoretically analyzes how GAN-based semi-supervised learning (GAN-SSL) works. We first prove that, given a fixed generator, optimizing the discriminator of GAN-SSL is equivalent to optimizing that of supervised learning. Thus, the optimal discriminator in GAN-SSL is expected to be perfect on labeled data. Then, if the perfect discriminator can further cause the optimization objective to reach its theoretical maximum, the optimal generator will match the true data distribution. Since it is impossible to reach the theoretical maximum in practice, one cannot expect to obtain a perfect generator for generating data, which is apparently different from the objective of GANs. Furthermore, if the labeled data can traverse all connected subdomains of the data manifold, which is reasonable in semi-supervised classification, we additionally expect the optimal discriminator in GAN-SSL to also be perfect on unlabeled data. In conclusion, the minimax optimization in GAN-SSL will theoretically output a perfect discriminator on both labeled and unlabeled data by unexpectedly learning an imperfect generator, i.e., GAN-SSL can effectively improve the generalization ability of the discriminator by leveraging unlabeled information.
