Regression with Label Permutation in Generalized Linear Model

Guanhua Fang, Ping Li
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:9716-9760, 2023.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-fang23a, title = {Regression with Label Permutation in Generalized Linear Model}, author = {Fang, Guanhua and Li, Ping}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {9716--9760}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/fang23a/fang23a.pdf}, url = {https://proceedings.mlr.press/v202/fang23a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Regression with Label Permutation in Generalized Linear Model %A Guanhua Fang %A Ping Li %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-fang23a %I PMLR %P 9716--9760 %U https://proceedings.mlr.press/v202/fang23a.html %V 202 %X 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.
APA
Fang, G. & Li, P.. (2023). Regression with Label Permutation in Generalized Linear Model. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:9716-9760 Available from https://proceedings.mlr.press/v202/fang23a.html.

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