## Abstract

Linear regression is one of the most prevalent techniques in machine learning; however, it is also common to use linear regression for its explanatory capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. Gender) and a label (e.g. Income) in the presence of other (potentially correlated) features. OLS assumes a particular model that randomly generates the data, and derives t-values-representing the likelihood of each real value to be the true correlation. Using i-values, OLS can release a confidence interval, which is an interval on the reals that is likely to contain the true correlation; and when this interval does not intersect the origin, we can reject the null hypothesis as it is likely that the true correlation is non-zero. Our work aims at achieving similar guarantees on data under differentially private estimators. First, we show that for well-spread data, the Gaussian Johnson-Lindenstrauss Transform (JLT) gives a very good approximation of t-values; secondly, when JLT approximates Ridge regression (linear regression with/2-rcgularization) wc derive, under certain conditions, confidence intervals using the projected data; lastly, we derive, under different conditions, confidence intervals for the "Analyze Gauss" algorithm (Dwork et al., 2014).

Original language | English |
---|---|

Title of host publication | 34th International Conference on Machine Learning, ICML 2017 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 4774-4801 |

Number of pages | 28 |

ISBN (Electronic) | 9781510855144 |

State | Published - 2017 |

Externally published | Yes |

Event | 34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia Duration: 6 Aug 2017 → 11 Aug 2017 |

### Publication series

Name | 34th International Conference on Machine Learning, ICML 2017 |
---|---|

Volume | 7 |

### Conference

Conference | 34th International Conference on Machine Learning, ICML 2017 |
---|---|

Country/Territory | Australia |

City | Sydney |

Period | 6/08/17 → 11/08/17 |

### Bibliographical note

Publisher Copyright:Copyright © 2017 by the authors.