Transport-based Counterfactual Models

• URL: http://arxiv.org/abs/2108.13025v1
• Date: Mon, 30 Aug 2021 07:28:19 GMT
• Title: Transport-based Counterfactual Models
• Authors: Lucas de Lara (IMT), Alberto Gonz\'alez-Sanz (IMT), Nicholas Asher (IRIT-MELODI, CNRS), Jean-Michel Loubes (IMT)
• Abstract summary: State-of-the-art models to compute counterfactuals are either unrealistic or unfeasible. We address the problem of designing realistic and feasible counterfactuals in the absence of a causal model. We argue that optimal transport theory defines relevant transport-based counterfactual models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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