Uncertainty Visualization via Low-Dimensional Posterior Projections

• URL: http://arxiv.org/abs/2312.07804v2
• Date: Sun, 12 May 2024 10:34:04 GMT
• Title: Uncertainty Visualization via Low-Dimensional Posterior Projections
• Authors: Omer Yair, Elias Nehme, Tomer Michaeli,
• Abstract summary: We introduce a new approach for estimating and visualizing posteriors by employing energy-based models (EBMs) over low-dimensional subspaces. We demonstrate the effectiveness of our method across a diverse range of datasets and image restoration problems.
• Score: 23.371244861123827
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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