Lipschitz三角流的尾部
Tails of Lipschitz Triangular Flows
摘要：
我们调查流行的流为基础的方法来捕捉尾部的目标密度的属性，通过研究这些流的方法作用于一个易于处理的源密度的三角形地图。我们发现，密度分位数函数的源和目标密度提供了一个精确的表征的斜率的转换所需的目标密度捕获尾巴。我们进一步表明，任何Lipschitz连续输运映射作用于源密度将导致密度与源类似的尾部属性，突出了复杂的源密度和足够表达的变换之间的权衡，以捕获目标密度的理想属性。随后，我们说明了像Real-NVP，MAF和Glow这样的流模型最初实现时缺乏捕获非高斯尾部分布的能力。我们规避这个问题，提出尾部自适应流组成的源分布，可以同时学习的三角形地图，以捕捉目标密度的尾部属性。我们进行了几个合成和现实世界的实验，以补充我们的理论研究结果。
英文摘要：
We investigate the ability of popular flow based methods to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterization of the slope of transformation required to capture tails in a target density. We further show that any Lipschitz-continuous transport map acting on a source density will result in a density with similar tail properties as the source, highlighting the trade-off between a complex source density and a sufficiently expressive transformation to capture desirable properties of a target density. Subsequently, we illustrate that flow models like Real-NVP, MAF, and Glow as implemented originally lack the ability to capture a distribution with non-Gaussian tails. We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density. We perform several synthetic and real-world experiments to compliment our theoretical findings.
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