论文标题
边缘尾部自适应归一化流动
Marginal Tail-Adaptive Normalizing Flows
论文作者
论文摘要
学习分配的尾巴行为是一个众所周知的困难问题。从定义上讲，尾部的样品数量很小，深层生成模型（例如归一化流量）倾向于专注于学习分布的身体。在本文中，我们专注于提高归一化流以正确捕获尾巴行为的能力，从而形成更准确的模型。我们证明，可以通过其基本分布的边缘的尾巴来控制自回归流的边际尾巴。这种理论上的见解使我们获得了一种基于灵活的基础分布和数据驱动的线性层的新型流。经验分析表明，所提出的方法提高了准确性（尤其是在分布的尾巴上），并且能够生成重尾数据。我们证明了它在天气和气候示例中的应用，其中捕获尾巴行为至关重要。
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.
