Fast Private Kernel Density Estimation via Locality Sensitive Quantization

Tal Wagner*, Yonatan Naamad, Nina Mishra

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

We study efficient mechanisms for differentially private kernel density estimation (DP-KDE). Prior work for the Gaussian kernel described algorithms that run in time exponential in the number of dimensions d. This paper breaks the exponential barrier, and shows how the KDE can privately be approximated in time linear in d, making it feasible for high-dimensional data. We also present improved bounds for low-dimensional data. Our results are obtained through a general framework, which we term Locality Sensitive Quantization (LSQ), for constructing private KDE mechanisms where existing KDE approximation techniques can be applied. It lets us leverage several efficient non-private KDE methods-like Random Fourier Features, the Fast Gauss Transform, and Locality Sensitive Hashing-and “privatize” them in a black-box manner. Our experiments demonstrate that our resulting DP-KDE mechanisms are fast and accurate on large datasets in both high and low dimensions.

Original languageEnglish
Pages (from-to)35339-35367
Number of pages29
JournalProceedings of Machine Learning Research
Volume202
StatePublished - 2023
Externally publishedYes
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: 23 Jul 202329 Jul 2023

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