Copula与边际流：将边际流从其联合点中分离出来
Copula & Marginal Flows: Disentangling the Marginal from its Joint
摘要：
深度生成网络（如GANs和规范化流）在图像生成等高维任务的背景下蓬勃发展。然而，到目前为止，精确的建模或外推的分布特性，如尾部渐近生成网络产生的是不可用的。在本文中，我们通过两个新颖的贡献在深度学习文献中首次解决了这个问题。首先，我们推导出可以由生成网络表示的尾部的上界，并证明了Lp空间相关的性质。在那里，我们特别表明，在各种情况下，最佳生成网络并不存在。其次，我们引入并提出Copula和边际生成流（CM流），允许对CDF的尾部和任何先验假设进行精确建模，直到近似的均匀分布。我们的数值结果支持CM流的使用。
英文摘要：
Deep generative networks such as GANs and normalizing flows flourish in the context of high-dimensional tasks such as image generation. However, so far exact modeling or extrapolation of distributional properties such as the tail asymptotics generated by a generative network is not available. In this paper, we address this issue for the first time in the deep learning literature by making two novel contributions. First, we derive upper bounds for the tails that can be expressed by a generative network and demonstrate Lp-space related properties. There we show specifically that in various situations an optimal generative network does not exist. Second, we introduce and propose copula and marginal generative flows (CM flows) which allow for an exact modeling of the tail and any prior assumption on the CDF up to an approximation of the uniform distribution. Our numerical results support the use of CM flows.
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。
