论文标题
通过最大似然密度比估计的概率差异的统一视角：桥接KL差异和积分概率指标
Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics
论文作者
论文摘要
本文从最大似然密度比率估计（DRE）的角度来看，kullback-leibler（KL） - 差异和积分概率指标（IPMS）提供了统一的观点。 KL-Divergence和IPM都广泛用于生成建模等应用中的各个领域。但是，对这些概念的统一理解仍未得到探索。在本文中，我们表明KL差异和IPM可以表示为仅通过采样方案而不同的最大似然，并使用此结果来得出IPMS的统一形式和轻松的估计方法。为了开发估计问题，我们构建了一个不受限制的最大似然估计器，以使用分层采样方案执行DRE。我们进一步提出了一种新型的概率差异，称为密度比指标（DRMS），该差异将KL-Divergence和IPMS插值。除这些发现外，我们还介绍了DRM的某些应用，例如DRE和生成的对抗网络。在实验中，我们验证了提出的方法的有效性。
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relaxed estimation method. To develop the estimation problem, we construct an unconstrained maximum likelihood estimator to perform DRE with a stratified sampling scheme. We further propose a novel class of probability divergences, called the Density Ratio Metrics (DRMs), that interpolates the KL-divergence and the IPMs. In addition to these findings, we also introduce some applications of the DRMs, such as DRE and generative adversarial networks. In experiments, we validate the effectiveness of our proposed methods.
