Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification

TL;DR

The paper introduces vsPAIR, a novel autoencoder architecture that efficiently solves inverse problems while providing interpretable uncertainty estimates through a paired, sparse, variational approach.

Contribution

It presents a new variational autoencoder framework that pairs standard and sparse encodings for inverse problems, enhancing interpretability and uncertainty quantification.

Findings

Effective in blind inpainting tasks

Accurate uncertainty estimation in computed tomography

Structured, interpretable latent representations

Abstract

Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest, connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting and computed tomography, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.