Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions-猫眼课题宝

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2021-01

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Todd P. Huster;Jeremy E. Cohen;Zinan Lin;Kevin S. Chan;Charles A. Kamhoua;Nandi O. Leslie;C. Chiang;Vyas Sekar

生成对抗网络（GAN）通常被称为“通用分布学习器”，但它们可以代表和学习什么样的分布仍然是一个悬而未决的问题。重尾分布在金融风险评估、物理学和流行病学等许多不同领域都很普遍。我们观察到现有的GAN架构在匹配重尾分布的渐近行为方面做得很差，我们发现这个问题源于它们的构造。此外，当面对重尾分布所特有的无穷矩和离群点之间的大距离时，常见的损失函数会产生不稳定或接近零的梯度。我们用Pareto GAN解决这些问题。Pareto GAN利用极值理论和神经网络的功能特性来学习与特征的边缘分布的渐近行为相匹配的分布。我们确定了标准损失函数的问题，并提出了使用替代度量空间，使稳定和有效的学习。最后，我们评估我们提出的方法在各种重尾数据集。

Generative adversarial networks (GANs) are often billed as"universal distribution learners", but precisely what distributions they can represent and learn is still an open question. Heavy-tailed distributions are prevalent in many different domains such as financial risk-assessment, physics, and epidemiology. We observe that existing GAN architectures do a poor job of matching the asymptotic behavior of heavy-tailed distributions, a problem that we show stems from their construction. Additionally, when faced with the infinite moments and large distances between outlier points that are characteristic of heavy-tailed distributions, common loss functions produce unstable or near-zero gradients. We address these problems with the Pareto GAN. A Pareto GAN leverages extreme value theory and the functional properties of neural networks to learn a distribution that matches the asymptotic behavior of the marginal distributions of the features. We identify issues with standard loss functions and propose the use of alternative metric spaces that enable stable and efficient learning. Finally, we evaluate our proposed approach on a variety of heavy-tailed datasets.

Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions

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