Exact Learning of Juntas from Membership Queries

Abstract

In this paper we study adaptive and non-adaptive exact learning of Juntas from membership queries. We use new techniques to find new bounds, narrow some of the gaps between the lower bounds and upper bounds and find new deterministic and randomized algorithms with small query and time complexities.Some of the bounds are tight in the sense that finding better ones either gives a breakthrough result in some long-standing combinatorial open problem or needs a new technique that is beyond the existing ones.

Exact learning from an honest teacher that answers membership queries

“…Therefore the class d-Junta is almost optimally learnable. Bshouty and Costa, [49], close the above gap and showed that…”

“…A better query complexity can be obtained from the reduction in [49]. See the following Table . The outputs of the above algorithms are the Fourier representation of the decision tree and, therefore, they are non-proper learning algorithms.…”

“…d-Junta: The class of d-Juntas is studied by Damaschke in [107,108,109] and Bshouty and Costa in [49]. In [108], Damaschke shows that…”

“…They also showed that randomness does not help improving the query complexity. See also other results for randomized algorithms in [49,107], optimal algorithms for small d with a constant number of rounds and bounds for the number of rounds in [49,109].…”

Exact learning of juntas from membership queries

“…Learning from membership queries, [1], has fueled the interest of many papers due to its diverse applications in various areas including group testing [2], pooling design for DNA sequencing [3], blood testing [4], functional genomics (molecular biology) [5], chemical reactions [6,7], multi-access channel communications [2,8], whole-genome shotgun sequencing [9], DNA physical mapping [10], game theory [11], program synthesis [12], channel leak testing, codes, VLSI testing and AIDS screening and many others as in [13] and the references therein. Generally, in domains where queries can be answered by a non-human annotator, e.g.…”