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STOC

2000

ACM

2000

ACM

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 ...

Related Content

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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