Differentially Private Joint Independence Test
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908307997851648 |
|---|---|
| author | Liu, Xingwei Chen, Yuexin Xu, Wangli |
| author_facet | Liu, Xingwei Chen, Yuexin Xu, Wangli |
| contents | Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) in the context of differential privacy. Given the limiting distribution of the empirical estimate of dHSIC is complicated Gaussian chaos, constructing tests in the non-privacy regime is typically based on permutation and bootstrap. To detect joint dependence in privacy, we propose a dHSIC-based testing procedure by employing a differentially private permutation methodology. Our method enjoys privacy guarantee, valid level and pointwise consistency, while the bootstrap counterpart suffers inconsistent power. We further investigate the uniform power of the proposed test in dHSIC metric and $L_2$ metric, indicating that the proposed test attains the minimax optimal power across different privacy regimes. As a byproduct, our results also contain the pointwise and uniform power of the non-private permutation dHSIC, addressing an unsolved question remained in Pfister et al. (2018). Both numerical simulations and real data analysis on causal inference suggest our proposed test performs well empirically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differentially Private Joint Independence Test Liu, Xingwei Chen, Yuexin Xu, Wangli Statistics Theory Cryptography and Security Machine Learning Methodology 62G10, 62H20 Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) in the context of differential privacy. Given the limiting distribution of the empirical estimate of dHSIC is complicated Gaussian chaos, constructing tests in the non-privacy regime is typically based on permutation and bootstrap. To detect joint dependence in privacy, we propose a dHSIC-based testing procedure by employing a differentially private permutation methodology. Our method enjoys privacy guarantee, valid level and pointwise consistency, while the bootstrap counterpart suffers inconsistent power. We further investigate the uniform power of the proposed test in dHSIC metric and $L_2$ metric, indicating that the proposed test attains the minimax optimal power across different privacy regimes. As a byproduct, our results also contain the pointwise and uniform power of the non-private permutation dHSIC, addressing an unsolved question remained in Pfister et al. (2018). Both numerical simulations and real data analysis on causal inference suggest our proposed test performs well empirically. |
| title | Differentially Private Joint Independence Test |
| topic | Statistics Theory Cryptography and Security Machine Learning Methodology 62G10, 62H20 |
| url | https://arxiv.org/abs/2503.18721 |