Shuffled Linear Regression via Spectral Matching

TL;DR

This paper introduces a spectral matching approach for large-scale shuffled linear regression that efficiently estimates permutations and latent features, outperforming existing methods in accuracy and applicability.

Contribution

We develop a novel spectral matching method for large-scale shuffled linear regression, enabling efficient permutation recovery and extending to image registration tasks.

Findings

Accurate permutation and feature estimation with sufficient samples.

Outperforms existing algorithms in synthetic and real-world experiments.

Effective in image registration and pose estimation scenarios.

Abstract

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches by jointly estimating the permutation, resulting in shuffled LS and shuffled LASSO formulations. Existing methods, constrained by the combinatorial complexity of permutation recovery, often address small-scale cases with limited measurements. In contrast, we focus on large-scale SLR, particularly suited for environments with abundant measurement samples. We propose a spectral matching method that efficiently resolves permutations by aligning spectral components of the measurement and feature covariances. Rigorous theoretical analyses demonstrate that our method achieves accurate estimates in both shuffled LS and shuffled LASSO settings, given a sufficient number of samples. Furthermore, we extend our approach to address simultaneous pose and correspondence estimation in image registration tasks. Experiments on synthetic datasets and real-world image registration scenarios show that our method outperforms existing algorithms in both estimation accuracy and registration performance.