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Noise-tolerant learning, the parity problem, and the statistical query model

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Noise-tolerant learning, the parity problem, and the statistical query model
We describe a slightly subexponential time algorithm for learning parity functions in the presence of random classification noise, a problem closely related to several cryptographic and coding problems. Our algorithm runs in polynomial time for the case of parity functions that depend on only the first O(log n log log n) bits of input, which provides the first known instance of an efficient noisetolerant algorithm for a concept class that is not learnable in the Statistical Query model of Kearns [1998]. Thus, we demonstrate that the set of problems learnable in the statistical query model is a strict subset of those problems learnable in the presence of noise in the PAC model. In coding-theory terms, what we give is a poly(n)-time algorithm for decoding linear k × n codes in the presence of random noise for the case of k = c log n log log n for some c > 0. (The case of k = O(log n) is trivial since one can just individually check each of the 2k possible messages and choose the ...
Avrim Blum, Adam Kalai, Hal Wasserman
Added 01 Aug 2010
Updated 01 Aug 2010
Type Conference
Year 2000
Where STOC
Authors Avrim Blum, Adam Kalai, Hal Wasserman
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