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Transport-based Counterfactual Models

Abstract

Counterfactual frameworks have grown popular in explainable and fair machine learning, as they offer a natural notion of causation. However, state-of-the-art models to compute counterfactuals are either unrealistic or unfeasible. In particular, while Pearl's causal inference provides appealing rules to calculate counterfactuals, it relies on a model that is unknown and hard to discover in practice. We address the problem of designing realistic and feasible counterfactuals in the absence of a causal model. We define transport-based counterfactual models as collections of joint probability distributions between observable distributions, and show their connection to causal counterfactuals. More specifically, we argue that optimal transport theory defines relevant transport-based counterfactual models, as they are numerically feasible, statistically-faithful, and can even coincide with causal counterfactual models. We illustrate the practicality of these models by defining sharper fairness criteria than typical group fairness conditions.
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Dates and versions

hal-03216124 , version 1 (04-05-2021)
hal-03216124 , version 2 (28-08-2021)
hal-03216124 , version 3 (06-01-2023)

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Cite

Lucas de Lara, Alberto González-Sanz, Nicholas Asher, Jean-Michel Loubes. Transport-based Counterfactual Models. 2021. ⟨hal-03216124v2⟩
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