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arXiv · 1405.1535

Learning Boolean Halfspaces with Small Weights from Membership Queries

Hasan Abasi·Ali Z. Abdi·Nader H. Bshouty
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Abstract

We consider the problem of proper learning a Boolean Halfspace with integer weights $\{0,1,\ldots,t\}$ from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks $n^{O(t^5)}$ membership queries where the best lower bound for the number of membership queries is $n^t$ [Learning Threshold Functions with Small Weights Using Membership Queries. COLT 1999] In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks $n^{O(t)}$ membership queries. We also give a non-adaptive proper learning algorithm that asks $n^{O(t^3)}$ membership queries.

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Hasan Abasi, Ali Z. Abdi, Nader H. Bshouty. 2014-05-07. Learning Boolean Halfspaces with Small Weights from Membership Queries. https://arxiv.org/abs/1405.1535

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