## Abstract

We introduce the notion of restricted sensitivity as an alternative to global and smooth sensitivity to improve accuracy in differentially private data analysis. The definition of restricted sensitivity is similar to that of global sensitivity except that instead of quantifying over all possible datasets, we take advantage of any beliefs about the dataset that a querier may have, to quantify over a restricted class of datasets. Specifically, given a query f and a hypothesis H about the structure of a dataset D, we show generically how to transform f into a new query f_{H} whose global sensitivity (over all datasets including those that do not satisfy H) matches the restricted sensitivity of the query f. Moreover, if the belief of the querier is correct (i.e., D ∈ H) then f_{H}(D) = f(D). If the belief is incorrect, then f_{H}(D) may be inaccurate. We demonstrate the usefulness of this notion by considering the task of answering queries regarding social-networks, which we model as a combination of a graph and a labeling of its vertices. In particular, while our generic procedure is computationally inefficient, for the specific definition of H as graphs of bounded degree, we exhibit efficient ways of constructing f_{H} using different projection-based techniques. We then analyze two important query classes: subgraph counting queries (e.g., number of triangles) and local profile queries (e.g., number of people who know a spy and a computer-scientist who know each other). We demonstrate that the restricted sensitivity of such queries can be significantly lower than their smooth sensitivity. Thus, using restricted sensitivity we can maintain privacy whether or not D ∈ H, while providing more accurate results in the event that H holds true.

Original language | English |
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Title of host publication | ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science |

Pages | 87-96 |

Number of pages | 10 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

Event | 2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013 - Berkeley, CA, United States Duration: 9 Jan 2013 → 12 Jan 2013 |

### Publication series

Name | ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science |
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### Conference

Conference | 2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013 |
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Country/Territory | United States |

City | Berkeley, CA |

Period | 9/01/13 → 12/01/13 |

## Keywords

- differential privacy
- social networks