Uncertainty Visualization via Low-Dimensional Posterior Projections
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| author | Yair, Omer Nehme, Elias Michaeli, Tomer |
| author_facet | Yair, Omer Nehme, Elias Michaeli, Tomer |
| contents | In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is encoded in the posterior distribution. However, for high-dimensional data, this distribution is challenging to visualize. In this work, we introduce a new approach for estimating and visualizing posteriors by employing energy-based models (EBMs) over low-dimensional subspaces. Specifically, we train a conditional EBM that receives an input measurement and a set of directions that span some low-dimensional subspace of solutions, and outputs the probability density function of the posterior within that space. We demonstrate the effectiveness of our method across a diverse range of datasets and image restoration problems, showcasing its strength in uncertainty quantification and visualization. As we show, our method outperforms a baseline that projects samples from a diffusion-based posterior sampler, while being orders of magnitude faster. Furthermore, it is more accurate than a baseline that assumes a Gaussian posterior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uncertainty Visualization via Low-Dimensional Posterior Projections Yair, Omer Nehme, Elias Michaeli, Tomer Computer Vision and Pattern Recognition In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is encoded in the posterior distribution. However, for high-dimensional data, this distribution is challenging to visualize. In this work, we introduce a new approach for estimating and visualizing posteriors by employing energy-based models (EBMs) over low-dimensional subspaces. Specifically, we train a conditional EBM that receives an input measurement and a set of directions that span some low-dimensional subspace of solutions, and outputs the probability density function of the posterior within that space. We demonstrate the effectiveness of our method across a diverse range of datasets and image restoration problems, showcasing its strength in uncertainty quantification and visualization. As we show, our method outperforms a baseline that projects samples from a diffusion-based posterior sampler, while being orders of magnitude faster. Furthermore, it is more accurate than a baseline that assumes a Gaussian posterior. |
| title | Uncertainty Visualization via Low-Dimensional Posterior Projections |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2312.07804 |