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Differentially Private Mean Embeddings with Random Features for Synthetic Data Generation

Abstract

We present a differentially private data generation paradigm using random feature representations of kernel mean embeddings when comparing the distribution of true data with that of synthetic data. We exploit the random feature representations for two important benefits. First, we require a very low privacy cost for training deep generative models. This is because unlike kernel-based distance metrics that require computing the kernel matrix on all pairs of true and synthetic datapoints, we can detach the data-dependent term from the term solely dependent on synthetic data. Hence, we need to perturb the data-dependent term once-for-all and then use it until the end of the generator training. Second, we can obtain ananalytic sensitivity of the kernel mean embedding as the random features are norm bounded by construction. This removes the necessity of hyper-parameter search for a clipping norm to handle the unknown sensitivity of a generator network. We provide several variants of our algorithm, differentially-private mean embeddings with random features (DP-MERF) to jointly generate labels and input features for datasets such as heterogeneous tabular data and image data. Our algorithm achieves better privacy-utility trade-offs than existing methods when tested on several datasets.

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