A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization

TL;DR

This paper introduces a paired autoencoder framework for inverse problems that leverages Bayes risk minimization, enabling efficient surrogate modeling and better performance with limited supervised data.

Contribution

The paper proposes a novel paired autoencoder approach that learns optimal mappings between latent spaces for inverse problems, with theoretical insights and improved performance over existing methods.

Findings

Outperforms existing methods when supervised training data is scarce.

Provides computationally cheap metrics to predict solution quality.

Connects autoencoder-based inverse modeling with Bayes risk minimization.

Abstract

In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are used to efficiently represent the input and target spaces separately and optimal mappings are learned between latent spaces, thus enabling forward and inverse surrogate mappings. We focus on interpretations using Bayes risk and empirical Bayes risk minimization, and we provide various theoretical results and connections to existing works on low-rank matrix approximations. Similar to end-to-end approaches, our paired approach creates a surrogate model for forward propagation and regularized inversion. However, our approach outperforms existing approaches in scenarios where training data for unsupervised learning are readily available but training pairs for supervised learning are scarce. Furthermore, we show that cheaply computable evaluation metrics are available through this framework and can be used to predict whether the solution for a new sample should be predicted well.