Hermite Polynomial Features for Private Data Generation

Margarita Vinaroz, Mohammad-Amin Charusaie, Frederik Harder, Kamil Adamczewski, Mi Jung Park

Proceedings of the 39th International Conference on Machine Learning, PMLR 162:22300-22324, 2022.

Abstract

Kernel mean embedding is a useful tool to compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially private data generation. A recent work, DP-MERF (Harder et al., 2021), proposes to approximate the kernel mean embedding of data distribution using finite-dimensional random features, which yields an analytically tractable sensitivity of approximate kernel mean embedding. However, the required number of random features in DP-MERF is excessively high, often ten thousand to a hundred thousand, which worsens the sensitivity of the approximate kernel mean embedding. To improve the sensitivity, we propose to replace random features with Hermite polynomial features. Unlike the random features, the Hermite polynomial features are ordered, where the features at the low orders contain more information on the distribution than those at the high orders. Hence, a relatively low order of Hermite polynomial features can more accurately approximate the mean embedding of the data distribution compared to a significantly higher number of random features. As a result, the Hermite polynomial features help us to improve the privacy-accuracy trade-off compared to DP-MERF, as demonstrated on several heterogeneous tabular datasets, as well as several image benchmark datasets.

Cite this Paper

BibTeX

@InProceedings{pmlr-v162-vinaroz22a,
title = {Hermite Polynomial Features for Private Data Generation},
author = {Vinaroz, Margarita and Charusaie, Mohammad-Amin and Harder, Frederik and Adamczewski, Kamil and Park, Mi Jung},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {22300--22324},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/vinaroz22a/vinaroz22a.pdf},
url = {https://proceedings.mlr.press/v162/vinaroz22a.html},
abstract = {Kernel mean embedding is a useful tool to compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially private data generation. A recent work, DP-MERF (Harder et al., 2021), proposes to approximate the kernel mean embedding of data distribution using finite-dimensional random features, which yields an analytically tractable sensitivity of approximate kernel mean embedding. However, the required number of random features in DP-MERF is excessively high, often ten thousand to a hundred thousand, which worsens the sensitivity of the approximate kernel mean embedding. To improve the sensitivity, we propose to replace random features with Hermite polynomial features. Unlike the random features, the Hermite polynomial features are ordered, where the features at the low orders contain more information on the distribution than those at the high orders. Hence, a relatively low order of Hermite polynomial features can more accurately approximate the mean embedding of the data distribution compared to a significantly higher number of random features. As a result, the Hermite polynomial features help us to improve the privacy-accuracy trade-off compared to DP-MERF, as demonstrated on several heterogeneous tabular datasets, as well as several image benchmark datasets.}
}

Endnote

%0 Conference Paper
%T Hermite Polynomial Features for Private Data Generation
%A Margarita Vinaroz
%A Mohammad-Amin Charusaie
%A Frederik Harder
%A Kamil Adamczewski
%A Mi Jung Park
%B Proceedings of the 39th International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2022
%E Kamalika Chaudhuri
%E Stefanie Jegelka
%E Le Song
%E Csaba Szepesvari
%E Gang Niu
%E Sivan Sabato
%F pmlr-v162-vinaroz22a
%I PMLR
%P 22300--22324
%U https://proceedings.mlr.press/v162/vinaroz22a.html
%V 162
%X Kernel mean embedding is a useful tool to compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially private data generation. A recent work, DP-MERF (Harder et al., 2021), proposes to approximate the kernel mean embedding of data distribution using finite-dimensional random features, which yields an analytically tractable sensitivity of approximate kernel mean embedding. However, the required number of random features in DP-MERF is excessively high, often ten thousand to a hundred thousand, which worsens the sensitivity of the approximate kernel mean embedding. To improve the sensitivity, we propose to replace random features with Hermite polynomial features. Unlike the random features, the Hermite polynomial features are ordered, where the features at the low orders contain more information on the distribution than those at the high orders. Hence, a relatively low order of Hermite polynomial features can more accurately approximate the mean embedding of the data distribution compared to a significantly higher number of random features. As a result, the Hermite polynomial features help us to improve the privacy-accuracy trade-off compared to DP-MERF, as demonstrated on several heterogeneous tabular datasets, as well as several image benchmark datasets.

APA

Vinaroz, M., Charusaie, M., Harder, F., Adamczewski, K. & Park, M.J.. (2022). Hermite Polynomial Features for Private Data Generation. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:22300-22324 Available from https://proceedings.mlr.press/v162/vinaroz22a.html.