提出一种衡量一维概率分布差异的新方法，可用于生成模型优化。
Transport f divergences
- 基于映射函数的Jacobi算子与凸函数构造新散度
- 具备不变性、凸性及变分表示等良好数学性质
- 适合用于生成模型中的分布对齐与评估
我们定义了一类用于衡量一维样本空间中概率密度函数差异的散度。该构造基于将一个密度通过映射函数推送到另一个密度时的Jacobi算子与凸函数。我们称这些信息度量为运输f-散度（transport f-divergences）。本文给出了运输f-散度的若干性质，包括不变性、凸性、变分表示形式以及关于映射函数的泰勒展开。同时提供了在生成模型中应用运输f-散度的实例。
原文摘要 · Abstract (English)
We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards one density to the other. We call these information measures transport f-divergences. We present several properties of transport $f$-divergences, including invariances, convexities, variational formulations, and Taylor expansions in terms of mapping functions. Examples of transport f-divergences in generative models are provided.
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