Hagemann, Paul;
Hertrich, Johannes;
Altekrüger, Fabian;
Beinert, Robert;
Chemseddine, Jannis;
Steidl, Gabriele;
(2024)
Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel.
In:
Proceedings of the Twelfth International Conference on Learning Representations : ICLR 2024.
ICLR: Vienna, Austria.
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Abstract
We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modelling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.
| Type: | Proceedings paper |
|---|---|
| Title: | Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel |
| Event: | The Twelfth International Conference on Learning Representations |
| Location: | Vienna |
| Dates: | 7 Jan 2024 - 11 Jul 2024 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://openreview.net/forum?id=YrXHEb2qMb |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Bayesian inverse Problems, MMD, Gradient Flows, Deep Learning |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10194632 |
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