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Title: on the Learnability of Counting Functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Homer, Steven Chen, Zhixiang |
| Copyright Year | 2007 |
| Abstract | We examine the learnability of concepts based on counting functions. A counting function is a generalization of a parity function in which the weighted sum of n inputs is tested for equivalence to some value k modulo N . The concepts we study therefore generalize many commonly studied boolean functions. We first show that disjunctions of counting functions (DOCFs) with modulus N are learnable by equivalence queries and determine the number of queries sufficient and necessary. We show that α(N)n + 1 equivalence queries are sufficient where α(N) = O(logN) is the sum of the exponents in the prime decomposition of N . When counting functions in the disjunction have distinct counting moduli {Ni}, we show that α(lcm(Ni))n + 1 equivalence queries are sufficient. We also give lower bounds on the number of equivalence queries required to learn diagonal DOCFs (and therefore general DOCFs) and provide a matching upper bound in the case of diagonal DOCFs. We then demonstrate how the additional power of membership queries allows improved learning in two different ways: (1) more efficient learning for some classes learnable with equivalence queries only, and (2) learnability of other classes not known to be learnable with equivalence queries only. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.cs.panam.edu/~chen/paperfile/colt_long_95.pdf |
| Alternate Webpage(s) | http://faculty.utrgv.edu/zhixiang.chen/paperfile/colt_long_95.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
