Approximate Inference with Wasserstein Gradient Flows

Charlie Frogner, Tomaso Poggio
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2581-2590, 2020.

Abstract

We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional. Existing methods for computing Wasserstein gradient flows rely on discretization of the domain of the diffusion, prohibiting their application to domains in more than several dimensions. We propose instead a discretization-free inference method that computes the Wasserstein gradient flow directly in a space of continuous functions. We characterize approximation properties of the proposed method and evaluate it on a nonlinear filtering task, finding performance comparable to the state-of-the-art for filtering diffusions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-frogner20a, title = {Approximate Inference with Wasserstein Gradient Flows}, author = {Frogner, Charlie and Poggio, Tomaso}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2581--2590}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/frogner20a/frogner20a.pdf}, url = {https://proceedings.mlr.press/v108/frogner20a.html}, abstract = {We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional. Existing methods for computing Wasserstein gradient flows rely on discretization of the domain of the diffusion, prohibiting their application to domains in more than several dimensions. We propose instead a discretization-free inference method that computes the Wasserstein gradient flow directly in a space of continuous functions. We characterize approximation properties of the proposed method and evaluate it on a nonlinear filtering task, finding performance comparable to the state-of-the-art for filtering diffusions.} }
Endnote
%0 Conference Paper %T Approximate Inference with Wasserstein Gradient Flows %A Charlie Frogner %A Tomaso Poggio %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-frogner20a %I PMLR %P 2581--2590 %U https://proceedings.mlr.press/v108/frogner20a.html %V 108 %X We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional. Existing methods for computing Wasserstein gradient flows rely on discretization of the domain of the diffusion, prohibiting their application to domains in more than several dimensions. We propose instead a discretization-free inference method that computes the Wasserstein gradient flow directly in a space of continuous functions. We characterize approximation properties of the proposed method and evaluate it on a nonlinear filtering task, finding performance comparable to the state-of-the-art for filtering diffusions.
APA
Frogner, C. & Poggio, T.. (2020). Approximate Inference with Wasserstein Gradient Flows. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2581-2590 Available from https://proceedings.mlr.press/v108/frogner20a.html.

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