Differentially Private Joint Independence Test
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差分隐私下的联合独立性检验
- 研究问题
- 当多个随机向量的数据包含敏感信息时，如何在差分隐私约束下检验联合独立性，并保持有效检验水平和良好功效？
- 方法与思路
- 作者基于多变量 Hilbert–Schmidt 独立性准则构造差分隐私置换检验，并在 dHSIC 与 L₂ 度量下分析一致性和统一功效。
- 材料陈述的贡献
- 摘要称，检验具有隐私保证、有效水平及点态一致性，并在不同隐私区间达到极小极大最优功效，同时补充非隐私检验的功效结果。
- 阅读关注点
- 应核对隐私定义、核函数与备择集合限制、置换机制及最优功效的比较基准，并辨明自助法功效不一致的具体情形。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未给出隐私预算和功效边界，不能将其结论推广到所有自助检验。
原文摘要
Identification of joint dependence among several 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 $d$-variable Hilbert-Schmidt independence criterion (dHSIC) in the context of differential privacy. Given that the limiting distribution of the empirical estimate of dHSIC is a complicated Gaussian chaos, constructing tests in the non-private regime is typically based on permutation and bootstrap methods. To detect joint dependence under privacy constraints, we propose a dHSIC-based testing procedure employing a differentially private permutation methodology. We show that our method enjoys privacy guarantees, a valid level, and pointwise consistency, whereas the bootstrap counterpart suffers from inconsistent power. We further investigate the uniform power of the proposed test under the dHSIC and $L_2$ metrics, showing that the proposed test attains the minimax optimal power across different privacy regimes. As a byproduct, we show that the non-private permutation dHSIC test proposed in Pfister et al. (2018) is a special case of our differentially private permutation test, and our results also establish its pointwise and uniform power--thus resolving an open problem from that work. Both numerical simulations and real data analysis in causal inference suggest that our proposed test performs well empirically.