Spread Divergence

Mingtian Zhang; Peter Hayes; Tom Bird; Raza Habib; David Barber

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arXiv · 1811.08968

Spread Divergence

Mingtian Zhang·Peter Hayes·Tom Bird·Raza Habib·David Barber

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Abstract

For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on modified $\mathbb{P}$ and $\mathbb{Q}$ and describe sufficient conditions for the existence of such a divergence. We demonstrate how to maximize the discriminatory power of a given divergence by parameterizing and learning the spread. We also give examples of using a Spread Divergence to train implicit generative models, including linear models (Independent Components Analysis) and non-linear models (Deep Generative Networks).

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stat.ML cs.LG

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Mingtian Zhang, Peter Hayes, Tom Bird, Raza Habib, David Barber. 2018-11-21. Spread Divergence. https://arxiv.org/abs/1811.08968

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