Transport f divergences

Wuchen Li

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arXiv · 2504.15515

Transport f divergences

Wuchen Li

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Abstract

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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Wuchen Li. 2025-04-22. Transport f divergences. https://arxiv.org/abs/2504.15515

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