A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization

2025-01-24

AI Summary

For scientific inverse problems characterized by scarce supervised paired data but abundant unpaired observations, this paper proposes the Paired Autoencoders (PAE) framework: two separate autoencoders are constructed for the input and target domains, with an optimal mapping learned between their latent spaces to jointly model forward and inverse processes. Crucially, training is guided by a Bayesian risk minimization principle, yielding the first PAE paradigm grounded in empirical Bayesian risk minimization. Theoretical analysis establishes an intrinsic connection to low-rank matrix approximation, ensuring high accuracy and robustness; PAE requires only minimal paired supervision and enables analytically tractable, a priori assessment of solution quality. Experiments demonstrate that PAE significantly outperforms end-to-end supervised methods in reconstruction accuracy, generalization efficiency, and uncertainty quantification.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• semi-supervised learning
• forward and inverse problems
• accuracy and efficiency enhancement

Innovation

• Paired Autoencoder
• Bayesian Risk Minimization
• Accuracy Assessment Metric