Support vector machines regression with unbounded sampling

ABSTRACT

Uniform boundedness of output variables is a standard assumption in most theoretical analysis of regression algorithms. This standard assumption has recently been weaken to a moment hypothesis in least square regression (LSR) setting. Although there has been a large literature on error analysis for LSR under the moment hypothesis, very little is known about the statistical properties of support vector machines regression with unbounded sampling. In this paper, we fill the gap in the literature. Without any restriction on the boundedness of the output sampling, we establish an ad hoc convergence analysis for support vector machines regression under very mild conditions.

KEYWORDS:

• Support vector machines regression
• unbounded sampling
• Hoeffding inequality
• learning rate

AMS SUBJECT CLASSIFICATIONS:

• 68T05
• 62J02

Acknowledgements

The authors thank the referees for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11571267], [grant number 11472315].