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Hermite Polynomial Features for Private Data Generation
Margarita Vinaroz · Mohammad-Amin Charusaie · Frederik Harder · Kamil Adamczewski · Mi Jung Park

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #1028

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 datageneration. 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 requirednumber 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 helpus to improve the privacy-accuracy trade-off compared to DP-MERF, as demonstrated on several heterogeneous tabular datasets, as well as severalimage benchmark datasets.

Author Information

Margarita Vinaroz (Max Planck Institute for Intelligent Systems and University of Tuebingen)
Mohammad-Amin Charusaie (Max-Planck-Institute for Intelligent Systems)
Frederik Harder (Max Planck Institute)
Kamil Adamczewski (Max Planck Institute for Intelligent Systems)
Mi Jung Park (UBC)

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