### Abstract

We show that all non-negative submodular functions have high noise-stability. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on {-1,1} ^{n} (for any constant accuracy parameter e). Our algorithm also succeeds in the agnostic setting. Previous work on learning submodular functions required either query access or strong assumptions about the types of submodular functions to be learned (and did not hold in the agnostic setting). Additionally we give simple algorithms that efficiently release differentially private answers to all Boolean conjunctions and to all halfspaces with constant average error, subsuming and improving recent work due to Gupta, Hardt, Roth and Ullman (STOC 2011).

Original language | English (US) |
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Title of host publication | Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 |

Publisher | Association for Computing Machinery |

Pages | 1586-1592 |

Number of pages | 7 |

ISBN (Print) | 9781611972108 |

DOIs | |

State | Published - 2012 |

Event | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 - Kyoto, Japan Duration: Jan 17 2012 → Jan 19 2012 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 |
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Country | Japan |

City | Kyoto |

Period | 1/17/12 → 1/19/12 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012*(pp. 1586-1592). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973099.126