Signal Strength Estimation in Logistic Regression Using Data Splitting

Weihao Li, Jun S. Liu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:68674-68720, 2026.

Abstract

Logistic regression is widely used in applications; however, when the dimension scales with the sample size, theory reveals that the asymptotic behavior of common M-estimators depends on nonzero bias and variance factors, which are functions of the signal strength. To leverage the theory to design valid statistical methodologies, it is essential to obtain accurate estimates of the signal strength. In this work, we utilize a data-splitting strategy to efficiently estimate the signal strength. To alleviate issues caused by separable data, we analyze the exact asymptotics of an M-estimator with a data-driven, non-decomposable regularizer that adapts to the true covariance structure. We justify the validity of our method through both theoretical analysis and numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-li26dn, title = {Signal Strength Estimation in Logistic Regression Using Data Splitting}, author = {Li, Weihao and Liu, Jun S.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {68674--68720}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/li26dn/li26dn.pdf}, url = {https://proceedings.mlr.press/v306/li26dn.html}, abstract = {Logistic regression is widely used in applications; however, when the dimension scales with the sample size, theory reveals that the asymptotic behavior of common M-estimators depends on nonzero bias and variance factors, which are functions of the signal strength. To leverage the theory to design valid statistical methodologies, it is essential to obtain accurate estimates of the signal strength. In this work, we utilize a data-splitting strategy to efficiently estimate the signal strength. To alleviate issues caused by separable data, we analyze the exact asymptotics of an M-estimator with a data-driven, non-decomposable regularizer that adapts to the true covariance structure. We justify the validity of our method through both theoretical analysis and numerical experiments.} }
Endnote
%0 Conference Paper %T Signal Strength Estimation in Logistic Regression Using Data Splitting %A Weihao Li %A Jun S. Liu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-li26dn %I PMLR %P 68674--68720 %U https://proceedings.mlr.press/v306/li26dn.html %V 306 %X Logistic regression is widely used in applications; however, when the dimension scales with the sample size, theory reveals that the asymptotic behavior of common M-estimators depends on nonzero bias and variance factors, which are functions of the signal strength. To leverage the theory to design valid statistical methodologies, it is essential to obtain accurate estimates of the signal strength. In this work, we utilize a data-splitting strategy to efficiently estimate the signal strength. To alleviate issues caused by separable data, we analyze the exact asymptotics of an M-estimator with a data-driven, non-decomposable regularizer that adapts to the true covariance structure. We justify the validity of our method through both theoretical analysis and numerical experiments.
APA
Li, W. & Liu, J.S.. (2026). Signal Strength Estimation in Logistic Regression Using Data Splitting. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:68674-68720 Available from https://proceedings.mlr.press/v306/li26dn.html.

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