On multiple-instance learning of halfspaces

被引：2

作者：

Diochnos, D. I. ^{[1
]}

Sloan, R. H. ^{[1
]}

Turan, Gy ^{[1
,2
,3
]}

机构：

[1] Univ Illinois, Chicago, IL 60607 USA

[2] Hungarian Acad Sci, Res Grp AI, H-1051 Budapest, Hungary

[3] Univ Szeged, Szeged, Hungary

来源：

INFORMATION PROCESSING LETTERS | 2012年 / 112卷 / 23期

基金：

美国国家科学基金会;

关键词：

Machine learning; Halfspaces; Multiple-instance learning; Cyclic polytopes; PAC learning; VC-dimension; Combinatorial problems;

D O I：

10.1016/j.ipl.2012.08.017

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In multiple-instance learning the learner receives bags, i.e., sets of instances. A bag is labeled positive if it contains a positive example of the target. An Omega(d logr) lower bound is given for the VC-dimension of bags of size r for d-dimensional halfspaces and it is shown that the same lower bound holds for halfspaces over any large point set in general position. This lower bound improves an Omega(logr) lower bound of Sabato and Tishby, and it is sharp in order of magnitude. We also show that the hypothesis finding problem is NP-complete and formulate several open problems. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：933 / 936

页数：4

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