Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909424697737216 |
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| author | He, Yiyun Strohmer, Thomas Vershynin, Roman Zhu, Yizhe |
| author_facet | He, Yiyun Strohmer, Thomas Vershynin, Roman Zhu, Yizhe |
| contents | Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_17148 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets He, Yiyun Strohmer, Thomas Vershynin, Roman Zhu, Yizhe Machine Learning Cryptography and Security Data Structures and Algorithms Probability Statistics Theory Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix. |
| title | Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets |
| topic | Machine Learning Cryptography and Security Data Structures and Algorithms Probability Statistics Theory |
| url | https://arxiv.org/abs/2305.17148 |