### Abstract

Consider an analyst who wants to release aggregate statistics about a data set containing sensitive information. Using differentially private algorithms guarantees that the released statistics reveal very little about any particular record in the data set. In this paper we study the asymptotic properties of differentially private algorithms for statistical inference. We show that for a large class of statistical estimators T and input distributions P, there is a differentially private estimator A_{T} with the same asymptotic distribution as T. That is, the random variables A_{T}(X) and T(X) converge in distribution when X consists of an i.i.d. sample from P of increasing size. This implies that A_{T}(X) is essentially as good as the original statistic T(X) for statistical inference, for sufficiently large samples. Our technique applies to (almost) any pair T,P such that T is asymptotically normal on i.i.d. samples from P - -in particular, to parametric maximum likelihood estimators and estimators for logistic and linear regression under standard regularity conditions. A consequence of our techniques is the existence of low-space streaming algorithms whose output converges to the same asymptotic distribution as a given estimator T (for the same class of estimators and input distributions as above).

Original language | English (US) |
---|---|

Title of host publication | STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing |

Pages | 813-821 |

Number of pages | 9 |

DOIs | |

State | Published - Jul 4 2011 |

Event | 43rd ACM Symposium on Theory of Computing, STOC'11 - San Jose, CA, United States Duration: Jun 6 2011 → Jun 8 2011 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
---|---|

ISSN (Print) | 0737-8017 |

### Other

Other | 43rd ACM Symposium on Theory of Computing, STOC'11 |
---|---|

Country | United States |

City | San Jose, CA |

Period | 6/6/11 → 6/8/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing*(pp. 813-821). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1993636.1993743