Exact learning of juntas from membership queries

ORACLES IN $\Sigma^p_2$ ARE SUFFFICIENT FOR EXACT LEARNING

International Journal of Foundations of Computer Science ◽

10.1142/s012905410000034x ◽

2000 ◽

Vol 11 (04) ◽

pp. 613-632 ◽

Cited By ~ 5

Author(s):

Johannes Köbler ◽

Wolfgang Lindner

Keyword(s):

Polynomial Time ◽

Learning Model ◽

Query Complexity ◽

Boolean Circuits ◽

Membership Queries ◽

Exact Learning ◽

Equivalence Queries

We study the learnability of representation classes in Angluin's exact learning model. In particular, we consider the following three query types: equivalence queries, equivalence and membership queries, and membership queries only. We show in all three cases that polynomial query complexity implies already polynomial-time learnability, provided that the learner additionally has access to an oracle in [Formula: see text]. It follows that boolean circuits are polynomial-time learnable with equivalence queries and the help of an oracle in [Formula: see text].a

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Exact learning of subclasses of CDNF formulas with membership queries

Lecture Notes in Computer Science - Computing and Combinatorics ◽

10.1007/3-540-61332-3_151 ◽

1996 ◽

pp. 179-188 ◽

Cited By ~ 1

Author(s):

Carlos Domingo

Keyword(s):

Membership Queries ◽

Exact Learning

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Two new results about quantum exact learning

Quantum ◽

10.22331/q-2021-11-24-587 ◽

2021 ◽

Vol 5 ◽

pp. 587

Author(s):

Srinivasan Arunachalam ◽

Sourav Chakraborty ◽

Troy Lee ◽

Manaswi Paraashar ◽

Ronald de Wolf

Keyword(s):

Boolean Function ◽

Upper Bound ◽

Boolean Functions ◽

Quantum Computers ◽

Concept Class ◽

Membership Queries ◽

Exact Learning ◽

Uniform Quantum

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a k-Fourier-sparse n-bit Boolean function from O(k1.5(log⁡k)2) uniform quantum examples for that function. This improves over the bound of Θ~(kn) uniformly random classical examples (Haviv and Regev, CCC'15). Additionally, we provide a possible direction to improve our O~(k1.5) upper bound by proving an improvement of Chang's lemma for k-Fourier-sparse Boolean functions. Second, we show that if a concept class C can be exactly learned using Q quantum membership queries, then it can also be learned using O(Q2log⁡Qlog⁡|C|)classical membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMP'04) by a log⁡Q-factor.

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On the Learnability of Possibilistic Theories

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/259 ◽

2020 ◽

Author(s):

Cosimo Persia ◽

Ana Ozaki

Keyword(s):

Large Class ◽

Polynomial Time ◽

Classical Logic ◽

Learning Model ◽

Membership Queries ◽

Exact Model ◽

Exact Learning ◽

Probably Approximately Correct ◽

Horn Theories ◽

Pac Model

We investigate learnability of possibilistic theories from entailments in light of Angluin’s exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct (PAC) model extended with membership queries, our work also establishes such results in this model.

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