Sequential Conditional (Marginally Optimal) Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness

With Agathe Fernandes Machado and Arthur Charpentier, we have uploaded our new working paper on arXiv : https://arxiv.org/abs/2408.03425

Abstract

In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, as suggested in Plečko and Meinshausen (2020)} and optimal transport, as in De Lara et al. (2024). We extend “Knothe’s rearrangement” Bonnotte (2013) and “triangular transport” Zech and Marzouk (2022) to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss individual fairness. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.

A replication ebook is available on Agathe’s Github Page: codes (ebook)

The corresponding R codes are available on Agathe’s GitHub: GitHub

In the background, level curves for \((x_1,x_2)\mapsto m(0,x_1,x_2)\) and \(m(1,x_1,x_2)\) respectively on the left and on the right. Then, on the left, individual \((s,x_1,x_2)=(s=0,-2,-1)\) (predicted 18.24% by model \(m\)), and on the right, visualization of two counterfactuals \((s=1,x_1^\star,x_2^\star)\) according to causal graphs 6a (bottom right path, predicted 40.94%) and 6b (top left path, predicted 54.06%).