## Annals of Functional Analysis

### Hypercircle Inequality for Partially-Corrupted Data

#### Abstract

In recent years, the problem of learning and methods for learning functions have received increasing attention in Machine Learning. This problem is motivated by several applications in which it is required to estimate a function representation from available data. Recently, an extension of hypercircle inequality to data error $(Hide)$ was proposed by Kannika Khompurngson and Charles A. Micchelli and the results on this subject have constructed a new learning method. Unfortunately, the material on Hide only applies to circumstances for which all data are known within error. In this paper, our purpose is to extend the hypercircle inequality to circumstances for which data set contains both accurate and inaccurate data.

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 95-108.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1419001453

Digital Object Identifier
doi:10.15352/afa/06-1-8

Mathematical Reviews number (MathSciNet)
MR3297790

Zentralblatt MATH identifier
1337.46023

#### Citation

Khompurngson, Kannika; Novaprateep, Boriboon. Hypercircle Inequality for Partially-Corrupted Data. Ann. Funct. Anal. 6 (2015), no. 1, 95--108. doi:10.15352/afa/06-1-8. https://projecteuclid.org/euclid.afa/1419001453

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