Uncertainty Visualization via Low-Dimensional Posterior Projections (2023-12-12T00:00:00.000000Z)

TL;DR

This work introduces a new approach for estimating and visualizing posteriors by em-ploying energy-based models (EBMs) over low-dimensional subspaces over low-dimensional subspaces by training 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.

Abstract

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible so-lutions, 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 em-ploying 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. Code is available at https://github.com/yairomer/PPDE.

Authors

Elias Nehme

2 papers

T. Michaeli

5 papers

Omer Yair

1 papers

TL;DR

Abstract

Authors

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