Learning boolean halfspaces with small weights from membership queries

Hasan Abasi; Ali Z. Abdi; Nader H. Bshouty

doi:10.1007/978-3-319-11662-4_8

Learning boolean halfspaces with small weights from membership queries

Hasan Abasi, Ali Z. Abdi, Nader H. Bshouty

Computer Science

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the problem of proper learning a Boolean Halfspace with integer weights {0, 1,…, t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t⁵) membership queries where the best lower bound for the number of membership queries is n^t [4].

In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t³) membership queries.

Original language	English
Title of host publication	Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings
Editors	Peter Auer, Alexander Clark, Thomas Zeugmann, Sandra Zilles
Pages	96-110
Number of pages	15
ISBN (Electronic)	9783319116617
DOIs	https://doi.org/10.1007/978-3-319-11662-4_8
State	Published - 2014
Event	25th International Conference on Algorithmic Learning Theory, ALT 2014 - Bled, Slovenia Duration: 8 Oct 2014 → 10 Oct 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8776

Conference

Conference	25th International Conference on Algorithmic Learning Theory, ALT 2014
Country/Territory	Slovenia
City	Bled
Period	8/10/14 → 10/10/14

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-11662-4_8

Cite this

Abasi, H., Abdi, A. Z., & Bshouty, N. H. (2014). Learning boolean halfspaces with small weights from membership queries. In P. Auer, A. Clark, T. Zeugmann, & S. Zilles (Eds.), Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings (pp. 96-110). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8776). https://doi.org/10.1007/978-3-319-11662-4_8

Abasi, Hasan ; Abdi, Ali Z. ; Bshouty, Nader H. / Learning boolean halfspaces with small weights from membership queries. Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings. editor / Peter Auer ; Alexander Clark ; Thomas Zeugmann ; Sandra Zilles. 2014. pp. 96-110 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{f86a5f167ab74f72a3e889e2bb4cae6d,

title = "Learning boolean halfspaces with small weights from membership queries",

abstract = "We consider the problem of proper learning a Boolean Halfspace with integer weights {0, 1,…, t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t5) membership queries where the best lower bound for the number of membership queries is nt [4].In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t3) membership queries.",

author = "Hasan Abasi and Abdi, {Ali Z.} and Bshouty, {Nader H.}",

note = "Publisher Copyright: {\textcopyright}Springer International Publishing Switzerland 2014.; 25th International Conference on Algorithmic Learning Theory, ALT 2014 ; Conference date: 08-10-2014 Through 10-10-2014",

year = "2014",

doi = "10.1007/978-3-319-11662-4_8",

language = "الإنجليزيّة",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Peter Auer and Alexander Clark and Thomas Zeugmann and Sandra Zilles",

booktitle = "Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings",

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Abasi, H, Abdi, AZ & Bshouty, NH 2014, Learning boolean halfspaces with small weights from membership queries. in P Auer, A Clark, T Zeugmann & S Zilles (eds), Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8776, pp. 96-110, 25th International Conference on Algorithmic Learning Theory, ALT 2014, Bled, Slovenia, 8/10/14. https://doi.org/10.1007/978-3-319-11662-4_8

Learning boolean halfspaces with small weights from membership queries. / Abasi, Hasan; Abdi, Ali Z.; Bshouty, Nader H.
Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings. ed. / Peter Auer; Alexander Clark; Thomas Zeugmann; Sandra Zilles. 2014. p. 96-110 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8776).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Bshouty, Nader H.

PY - 2014

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N2 - We consider the problem of proper learning a Boolean Halfspace with integer weights {0, 1,…, t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t5) membership queries where the best lower bound for the number of membership queries is nt [4].In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t3) membership queries.

AB - We consider the problem of proper learning a Boolean Halfspace with integer weights {0, 1,…, t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t5) membership queries where the best lower bound for the number of membership queries is nt [4].In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t3) membership queries.

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DO - 10.1007/978-3-319-11662-4_8

M3 - منشور من مؤتمر

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings

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T2 - 25th International Conference on Algorithmic Learning Theory, ALT 2014

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Abasi H, Abdi AZ, Bshouty NH. Learning boolean halfspaces with small weights from membership queries. In Auer P, Clark A, Zeugmann T, Zilles S, editors, Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings. 2014. p. 96-110. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-11662-4_8

Learning boolean halfspaces with small weights from membership queries

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