Transport f divergences
This work provides a theoretical framework for comparing probability densities, potentially useful in generative models, but appears incremental as it builds on existing divergence concepts.
The paper introduces transport f-divergences, a class of divergences for measuring differences between probability density functions in one-dimensional spaces, based on convex functions and Jacobi operators of mapping functions, and presents properties like invariances, convexities, and variational formulations.
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.