Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910376836202496 |
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| author | Hagemann, Paul Hertrich, Johannes Altekrüger, Fabian Beinert, Robert Chemseddine, Jannis Steidl, Gabriele |
| author_facet | Hagemann, Paul Hertrich, Johannes Altekrüger, Fabian Beinert, Robert Chemseddine, Jannis Steidl, Gabriele |
| contents | We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel Hagemann, Paul Hertrich, Johannes Altekrüger, Fabian Beinert, Robert Chemseddine, Jannis Steidl, Gabriele Machine Learning Optimization and Control Probability We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. 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. |
| title | Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel |
| topic | Machine Learning Optimization and Control Probability |
| url | https://arxiv.org/abs/2310.03054 |