ECP Reading Tools

A note on the richness of convex hulls of VC classes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A note on the richness of convex hulls of VC classes
2.	Creator	Author's name, affiliation, country	Gábor Lugosi; Pompeu Fabra University, Spain
2.	Creator	Author's name, affiliation, country	Shahar Mendelson; The Australian National University, Australia
2.	Creator	Author's name, affiliation, country	Vladimir Koltchinskii; The University of New Mexico, USA
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We prove the existence of a class $A$ of subsets of $\mathbb{R}^d$ of VC dimension 1 such that the symmetric convex hull $F$ of the class of characteristic functions of sets in $A$ is rich in the following sense. For any absolutely continuous probability measure $\mu$ on $\mathbb{R}^d$, measurable set $B$ and $\varepsilon > 0$, there exists a function $f$ in $F$ such that the measure of the symmetric difference of $B$ and the set where $f$ is positive is less than $\varepsilon$. The question was motivated by the investigation of the theoretical properties of certain algorithms in machine learning.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-12-17
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1097
10.	Identifier	Digital Object Identifier	10.1214/ECP.v8-1097
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.