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Calibration of [formula omitted]insensitive loss in support vector machines regression.
- Source :
-
Journal of the Franklin Institute . Mar2019, Vol. 356 Issue 4, p2111-2129. 19p. - Publication Year :
- 2019
-
Abstract
- Abstract 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CALIBRATION
*SUPPORT vector machines
*REGRESSION analysis
*NOISE
*DATA analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00160032
- Volume :
- 356
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of the Franklin Institute
- Publication Type :
- Periodical
- Accession number :
- 134884299
- Full Text :
- https://doi.org/10.1016/j.jfranklin.2018.11.021