Denoising linear models with permuted data

Ashwin Pananjady, Martin J. Wainwright, Thomas A. Courtade

Abstract: We consider the multivariate linear regression model with shuffled data and additive noise, which arises in various correspondence estimation and matching problems. We focus on the denoising problem and characterize the minimax error rate up to logarithmic factors. We also analyze the performance of two versions of a computationally efficient estimator that are consistent for a large range of input parameters. Finally, we provide an exact algorithm for the noiseless problem and demonstrate its performance on an image point-cloud matching task. Our analysis also extends to datasets with missing data.