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 OPT NAD (d-Junta) = O(d2 d log n).…”

“…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].…”

Subspace restrictions and affine composition for covering perfect hash families

“…We develop effective construction techniques for combinatorial arrays called covering perfect hash families, which form a compact representation of covering arrays. Covering arrays arise in numerous applications in which interactions among options or factors are to be measured; they are used in, for example, software testing [12,13], hardware testing [10,20], design of composite materials [2], computational learning [1,9], and biological networks [14]. Computational methods to construct covering arrays often encounter difficulties when the array has many rows, many columns, or both.…”