Pairwise Maximum Likelihood For Multi-Class Logistic Regression Model With Multiple Rare Classes

Xuetong Li, Danyang Huang, Hansheng Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:34725-34741, 2025.

Abstract

We study in this work the problem of multi-class logistic regression with one major class and multiple rare classes, which is motivated by a real application in TikTok live stream data. The model is inspired by the two-class logistic regression model of Wang (2020) but with surprising theoretical findings, which in turn motivate new estimation methods with excellent statistical and computational efficiency. Specifically, since rigorous theoretical analysis suggests that the resulting maximum likelihood estimators of different rare classes should be asymptotically independent, we consider to solve multiple pairwise two-class logistic regression problems instead of optimizing the joint log-likelihood function with computational challenge in multi-class problem, which are computationally much easier and can be conducted in a fully parallel way. To further reduce the computation cost, a subsample-based pairwise likelihood estimator is developed by down-sampling the major class. We show rigorously that the resulting estimators could be as asymptotically efficient as the global maximum likelihood estimator under appropriate regularity conditions. Extensive simulation studies are presented to support our theoretical findings and a TikTok live stream dataset is analyzed for illustration purpose.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-li25ag, title = {Pairwise Maximum Likelihood For Multi-Class Logistic Regression Model With Multiple Rare Classes}, author = {Li, Xuetong and Huang, Danyang and Wang, Hansheng}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {34725--34741}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/li25ag/li25ag.pdf}, url = {https://proceedings.mlr.press/v267/li25ag.html}, abstract = {We study in this work the problem of multi-class logistic regression with one major class and multiple rare classes, which is motivated by a real application in TikTok live stream data. The model is inspired by the two-class logistic regression model of Wang (2020) but with surprising theoretical findings, which in turn motivate new estimation methods with excellent statistical and computational efficiency. Specifically, since rigorous theoretical analysis suggests that the resulting maximum likelihood estimators of different rare classes should be asymptotically independent, we consider to solve multiple pairwise two-class logistic regression problems instead of optimizing the joint log-likelihood function with computational challenge in multi-class problem, which are computationally much easier and can be conducted in a fully parallel way. To further reduce the computation cost, a subsample-based pairwise likelihood estimator is developed by down-sampling the major class. We show rigorously that the resulting estimators could be as asymptotically efficient as the global maximum likelihood estimator under appropriate regularity conditions. Extensive simulation studies are presented to support our theoretical findings and a TikTok live stream dataset is analyzed for illustration purpose.} }
Endnote
%0 Conference Paper %T Pairwise Maximum Likelihood For Multi-Class Logistic Regression Model With Multiple Rare Classes %A Xuetong Li %A Danyang Huang %A Hansheng Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-li25ag %I PMLR %P 34725--34741 %U https://proceedings.mlr.press/v267/li25ag.html %V 267 %X We study in this work the problem of multi-class logistic regression with one major class and multiple rare classes, which is motivated by a real application in TikTok live stream data. The model is inspired by the two-class logistic regression model of Wang (2020) but with surprising theoretical findings, which in turn motivate new estimation methods with excellent statistical and computational efficiency. Specifically, since rigorous theoretical analysis suggests that the resulting maximum likelihood estimators of different rare classes should be asymptotically independent, we consider to solve multiple pairwise two-class logistic regression problems instead of optimizing the joint log-likelihood function with computational challenge in multi-class problem, which are computationally much easier and can be conducted in a fully parallel way. To further reduce the computation cost, a subsample-based pairwise likelihood estimator is developed by down-sampling the major class. We show rigorously that the resulting estimators could be as asymptotically efficient as the global maximum likelihood estimator under appropriate regularity conditions. Extensive simulation studies are presented to support our theoretical findings and a TikTok live stream dataset is analyzed for illustration purpose.
APA
Li, X., Huang, D. & Wang, H.. (2025). Pairwise Maximum Likelihood For Multi-Class Logistic Regression Model With Multiple Rare Classes. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:34725-34741 Available from https://proceedings.mlr.press/v267/li25ag.html.

Related Material