Differentially Private Sampling from Distributions via Wasserstein Projection
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918494015062016 |
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| author | Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi |
| author_facet | Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi |
| contents | In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such formulations suffer from two key limitations: 1) they fail to capture the geometric structure of the support, and 2) they are not applicable when the supports of the distributions differ. To deal with these issues, we develop a novel framework for DP sampling with Wasserstein distance as the utility measure. In this formulation, we propose Wasserstein Projection Mechanism (WPM), a minimax optimal mechanism based on Wasserstein projection. Furthermore, we develop efficient algorithms for computing the proposed mechanisms approximately and provide convergence guarantees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10015 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Differentially Private Sampling from Distributions via Wasserstein Projection Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi Machine Learning Cryptography and Security In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such formulations suffer from two key limitations: 1) they fail to capture the geometric structure of the support, and 2) they are not applicable when the supports of the distributions differ. To deal with these issues, we develop a novel framework for DP sampling with Wasserstein distance as the utility measure. In this formulation, we propose Wasserstein Projection Mechanism (WPM), a minimax optimal mechanism based on Wasserstein projection. Furthermore, we develop efficient algorithms for computing the proposed mechanisms approximately and provide convergence guarantees. |
| title | Differentially Private Sampling from Distributions via Wasserstein Projection |
| topic | Machine Learning Cryptography and Security |
| url | https://arxiv.org/abs/2605.10015 |