SPLICE: Differentially Private Synthetic Data with Dimension-Independent Guarantees
Original title: Differentially Private Synthetic Data from Sliced Chebyshev Moments
SPLICE returns a private distribution with Sliced Wasserstein-1 distance tilde O(1/sqrt(n)) from the target, independent of data dimension d.
The paper presents SPLICE, a new differentially private synthetic data algorithm based on noisy sliced Chebyshev polynomial moments. It fits a distribution to match these moments and provides global distributional guarantees without exponential dependence on dimension d. For a dataset of n examples, SPLICE returns a private distribution at distance tilde O(1/sqrt(n)) from the target, and a practical implementation using tensor decomposition tools achieves state-of-the-art performance on benchmarks.
- SPLICE uses sliced Chebyshev moments along random directions.
- Matching O(1/alpha) moments along tilde O(d/alpha^2) directions guarantees alpha Sliced Wasserstein error.
- Error bound tilde O(1/sqrt(n)) is independent of data dimension d.
- Tensor decomposition tools enable practical implementation.
From the original article
1 min read at arxiv.orgResearch on practical differentially private (DP) synthetic data has largely focused on methods that approximately preserve low-dimensional marginals of a target distribution, and can thus only hope to preserve higher-dimensional, global structure as a lucky by-product. At the same time, existing methods that target global accuracy guarantees pay a price exponential in the data dimension, $d$.
By Lucas Rosenblatt · arxiv.org
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