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On learning counting functions with queries (1994)
| Venue: | in "7th Annual ACM Conference on Computational Learning Theory, COLT'94 |
| Citations: | 4 - 2 self |
BibTeX
@INPROCEEDINGS{Homer94onlearning,
author = {Steven Homer and Zhixiang Chen Y},
title = {On learning counting functions with queries},
booktitle = {in "7th Annual ACM Conference on Computational Learning Theory, COLT'94},
year = {1994},
pages = {218--227},
publisher = {Press}
}
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Abstract
We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Zn q (or Zn) for any given integer q 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary eld. In general a counting function mayhavea composite modulus. We prove that, for any given integer q 2, over the domain Z n 2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Booleanweighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions. 1
