基于连续敏感属性的公平表示学习的联合分布路径

中文摘要 AI 辅助

带有连续敏感属性 $S$ 的公平表示学习需要表示 $Z$ 与 $S$ 统计独立。现有准则包括广义人口 parity、积分概率度量期望（EIPM）和互信息，它们通过对 $S$ 的分布求平均，来强制条件分布 $P_{Z \mid S=s}$ 与边缘分布 $P_Z$ 之间的逐值差异，该方法需要为每个敏感值的条件分布提供非参数替代。我们提出通过联合分布 $P_{Z, S}$ 与其边缘乘积 $P_Z \otimes P_S$ 之间的单一联合差异 $d(P_{Z, S}, P_Z \otimes P_S)$ 来评估独立性。我们建立了分解恒等式：在可分解见证类上，该差异等于 EIPM 和广义人口 parity 所实例化的条件积分泛函。由于无需条件分布即可达到相同目标，该差异可通过依赖统计量直接从样本中估计，而非通过条件平滑。我们以希尔伯特-施密特依赖准则（HSIC）作为联合差异 $d$ 的实例，研究替换条件路径的统计效率：HSIC 估计器是闭式 $O(n^2)$ 统计量，收敛速度为 $O(n^{-1/2})$，相比之下，条件路径估计器的非参数收敛速度为 $O(n^{-2/5})$。我们证明该实例在显式谱尾范围内等价于条件最大均值差异（MMD）积分，对应的算法实现 FRHSIC 达到了与条件路径基准相当的公平性-准确性权衡，同时减少了每轮训练时间。

英文摘要

Fair representation learning with a continuous sensitive attribute $S$ requires a representation $Z$ that is statistically independent of $S$. Existing criteria, including generalized demographic parity, the expectation of integral probability metrics (EIPM), and mutual information, enforce this independence by averaging a per-value discrepancy between the conditional law $P_{Z \mid S=s}$ and the marginal $P_Z$ over the law of $S$. This approach requires a nonparametric surrogate for the conditional law at each sensitive value. We propose evaluating independence through a single joint discrepancy $d\left(P_{Z, S}, P_Z \otimes P_S\right)$ between the joint law and the product of its marginals. We establish a disintegration identity; on decomposable witness classes it equals the conditional-integral functional that EIPM and generalized demographic parity instantiate. By reaching the same target without the conditional law, this discrepancy can be estimated directly from samples via a dependence statistic rather than conditional smoothing. We take the Hilbert-Schmidt independence criterion (HSIC) as an instance of the joint discrepancy $d$ to investigate the statistical efficiency of replacing the conditional formulation. The HSIC estimator is a closed-form $O\left(n^2\right)$ statistic that converges at the $O\left(n^{-1 / 2}\right)$ rate, in contrast to the nonparametric $O\left(n^{-2 / 5}\right)$ rate of the conditional-route estimators. We prove this instance is equivalent to the conditional maximum mean discrepancy (MMD) integral up to an explicit spectral tail. The corresponding algorithmic implementation, i.e., FRHSIC, attains fairness-accuracy tradeoffs comparable to conditional-route basel es while reducing per-epoch training time.

发表机构

• Georgia Institute of Technology（佐治亚理工学院）

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