Simplex-based multinomial logistic regression with diverging numbers of categories and covariate

Sheng Fu, Piao Chen*, Yufeng Liu, Zhisheng Ye

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


Multinomial logistic regression models are popular in multicategory classification analysis, but existing models suffer several intrinsic drawbacks. In particular, the parameters cannot be determined uniquely because of the over-specification. Although additional constraints have been imposed to refine the model, such modifications can be inefficient and complicated. In this paper, we propose a novel and efficient simplex-based multinomial logistic regression technique, seamlessly connecting binomial and multinomial cases under a unified framework. Compared with existing models, our model has fewer parameters, is free of any constraints, and can be solved efficiently using the Fisher scoring algorithm. In addition, the proposed model enjoys several theoretical advantages, including Fisher consistency and sharp comparison inequality. Under mild conditions, we establish the asymptotical normality and convergence for the new model, even when the numbers of categories and covariates increase with the sample size. The proposed framework is illustrated by means of extensive simulations and real applications.

Original languageEnglish
Pages (from-to)2463-2493
Number of pages31
JournalStatistica Sinica
Issue number4
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Asymptotics
  • classification
  • Fisher consistency
  • kernel learning
  • MLR
  • simplex coding scheme


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