用组合数据与狄利克雷传输解决类别变量反事实推断难题
Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport
- 将类别变量转为单纯形上的组合数据进行运输
- 在真实数据上验证了方法的有效性与可解释性
- 适合关注个体层面公平性的研究人员使用
近期基于最优传输的反事实推断方法受到关注，用于量化算法偏见。但在多变量场景中，这些方法常缺乏可解释性。已有研究结合因果图与迭代分位数回归（Plečko and Meinshausen, 2020），或顺序传输（Fernandes Machado et al., 2025）实现个体层面公平性分析，即“反事实公平性”。然而，类别变量的传输仍是实际应用中的关键挑战。本文提出新方法：首先将类别变量转化为组合数据，其次在 ℝ^d 的概率单纯形内进行狄利克雷传输。通过真实数据示例展示了该方法的适用性与有效性，并讨论其局限性。
原文摘要 · Abstract (English)
Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to interpret. To address this, alternative methodologies have been proposed, using causal graphs combined with iterative quantile regressions (Plečko and Meinshausen (2020)) or sequential transport (Fernandes Machado et al. (2025)) to examine fairness at the individual level, often referred to as ``counterfactual fairness.'' Despite these advancements, transporting categorical variables remains a significant challenge in practical applications with real datasets. In this paper, we propose a novel approach to address this issue. Our method involves (1) converting categorical variables into compositional data and (2) transporting these compositions within the probabilistic simplex of $\mathbb{R}^d$. We demonstrate the applicability and effectiveness of this approach through an illustration on real-world data, and discuss limitations.
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