# Regression with Label Permutation in Generalized Linear Model

arXiv: https://arxiv.org/abs/2206.11775 · HTML: https://mlsanity.com/paper/2206.11775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [Sparse Recovery with Shuffled Labels: Statistical Limits and Practical Estimators](https://mlsanity.com/paper/2303.11233/) (2023)
- [Optimal Estimator for Linear Regression with Shuffled Labels](https://mlsanity.com/paper/2310.01326/) (2023)

## Abstract (arXiv)

The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing attentions in the recent literature. In this paper, we present a relatively complete analysis of label permutation problem for the generalized linear model with multivariate responses. The theory is established under different scenarios, with knowledge of true parameters, with partial knowledge of underlying label permutation matrix and without any knowledge. Our results remove the stringent conditions required by the current literature and are further extended to the missing observation setting which has never been considered in the field of label permutation problem. On computational side, we propose two methods, "maximum likelihood estimation" algorithm and "two-step estimation" algorithm, to accommodate for different settings. When the proportion of permuted labels is moderate, both methods work effectively. Multiple numerical experiments are provided and corroborate our theoretical findings.