关于相对论性$f$ -发散
On Relativistic $f$-Divergences
摘要：
本文对相对论性生成对抗网络（RGAN）进行了更严格的研究。我们证明了该方法的目标函数是具有极小性质的凹函数$f$（$f(0)=0$，$f'(0) \neq 0$，$\sup_x f(x)>0$）的统计发散.我们还设计了相对论性$f$ -发散的几个变体。Wasserstein GAN最初是由Wasserstein距离（WD）是最合理的，因为它是弱的（即，它导致弱拓扑）。我们证明了WD比$f$ -发散弱，而后者又比相对论性$f$ -发散弱。考虑到RGAN的良好性能，这表明WGAN表现不佳主要是因为弱度量，而是因为正则化和相对论性正则化的使用。我们还仔细研究了相对论性$f$ -发散的估计。我们为相对论配对GANs（RpGANs;最初称为RGANs，可能会带来混乱）引入最小方差无偏估计（MVUE），并表明它并没有表现得更好。此外，我们证明了相对论平均GANs（RaGAN）的估计量仅是渐近无偏的，但有限样本偏差很小。消除这种偏差并不能提高性能。
英文摘要：
This paper provides a more rigorous look at Relativistic Generative Adversarial Networks (RGANs). We prove that the objective function of the discriminator is a statistical divergence for any concave function $f$ with minimal properties ($f(0)=0$, $f'(0) \neq 0$, $\sup_x f(x)>0$). We also devise a few variants of relativistic $f$-divergences. Wasserstein GAN was originally justified by the idea that the Wasserstein distance (WD) is most sensible because it is weak (i.e., it induces a weak topology). We show that the WD is weaker than $f$-divergences which are weaker than relativistic $f$-divergences. Given the good performance of RGANs, this suggests that WGAN does not performs well primarily because of the weak metric, but rather because of regularization and the use of a relativistic discriminator. We also take a closer look at estimators of relativistic $f$-divergences. We introduce the minimum-variance unbiased estimator (MVUE) for Relativistic paired GANs (RpGANs; originally called RGANs which could bring confusion) and show that it does not perform better. Furthermore, we show that the estimator of Relativistic average GANs (RaGANs) is only asymptotically unbiased, but that the finite-sample bias is small. Removing this bias does not improve performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
