Linear Algorithms for Robust and Scalable Nonparametric Multiclass Probability Estimation

Zeng, Liyun; Zhang, Hao Helen

doi:10.6339/22-JDS1069

Journal of Data Science

Linear Algorithms for Robust and Scalable Nonparametric Multiclass Probability Estimation

Volume 21, Issue 4 (2023), pp. 658–680

Liyun Zeng Hao Helen Zhang

https://doi.org/10.6339/22-JDS1069

Pub. online: 3 November 2022 Type: Statistical Data Science

Open Access

Received
3 June 2022

Accepted
25 September 2022

Published
3 November 2022

Abstract

Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a class of weighted Support Vector Machines (wSVMs) has been developed to estimate class probabilities through ensemble learning for K-class problems (Wu et al., 2010; Wang et al., 2019), where K is the number of classes. The estimators are robust and achieve high accuracy for probability estimation, but their learning is implemented through pairwise coupling, which demands polynomial time in K. In this paper, we propose two new learning schemes, the baseline learning and the One-vs-All (OVA) learning, to further improve wSVMs in terms of computational efficiency and estimation accuracy. In particular, the baseline learning has optimal computational complexity in the sense that it is linear in K. Though not the most efficient in computation, the OVA is found to have the best estimation accuracy among all the procedures under comparison. The resulting estimators are distribution-free and shown to be consistent. We further conduct extensive numerical experiments to demonstrate their finite sample performance.

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2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

linear time algorithm multiclass classification non-parametric probability estimation scalability support vector machines

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