A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution. We give a probabilistic interpretation of the network parameters of ACNet and use this to derive a simple but efficient sampling algorithm for the learned copula. Our experiments show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.

翻译：在机器学习和统计方面,一个中心问题是模拟数据随机变量的联合密度。Copula是具有统一的边际分布的合并累积分布功能,用来在与边际分离的情况下捕捉相互依存关系。Copula在统计中被广泛使用,但在现代深层学习中没有得到牵引。在本文中,我们引入了ACNet,这是一个新型的可差异神经网络结构结构结构结构结构结构结构结构,使人们能够学习重要的千叶-亚甲基底科普拉类。与Generation Aversarial 网络、Varitional Autencoders或正常流动方法不同,后者直接学习密度或基因过程,ACNet学会了千叶的生成器,它暗含了联合分布的累积分布功能。我们对ACNet的网络参数进行概率性解释,并以此为学习的椰子提供简单而高效的抽样算法。我们的实验表明,ACNet既能够接近普通的Archimedean Copulas,又能够产生更适合的数据。