Calibration of ϵ−insensitive loss in support vector machines regression

Hongzhi Tong, Kwok Po NG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


Support vector machines regression (SVMR) is an important tool in many machine learning applications. In this paper, we focus on the theoretical understanding of SVMR based on the ϵ−insensitive loss. For fixed ϵ ≥ 0 and general data generating distributions, we show that the minimizer of the expected risk for ϵ−insensitive loss used in SVMR is a set-valued function called conditional ϵ−median. We then establish a calibration inequality of ϵ−insensitive loss under a noise condition on the conditional distributions. This inequality also ensures us to present a nontrivial variance-expectation bound for ϵ−insensitive loss, and which is known to be important in statistical analysis of the regularized learning algorithms. With the help of the calibration inequality and variance-expectation bound, we finally derive an explicit learning rate for SVMR in some L r −space.

Original languageEnglish
Pages (from-to)2111-2129
Number of pages19
JournalJournal of the Franklin Institute
Issue number4
Publication statusPublished - Mar 2019

Scopus Subject Areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics


Dive into the research topics of 'Calibration of ϵ−insensitive loss in support vector machines regression'. Together they form a unique fingerprint.

Cite this