[Paper Review] Transport-based Counterfactual Models

de Lara, Lucas, González-Sanz, Alberto+3 more|arXiv (Cornell University)|Aug 30, 2021

Ethics and Social Impacts of AI67 references57 citations

TL;DR

The paper proposes transport-based counterfactual models that replace unknown causal models with optimal transport couplings to generate realistic, in-distribution counterfactuals and enable feasible fairness applications.

ABSTRACT

Counterfactual frameworks have grown popular in machine learning for both explaining algorithmic decisions but also defining individual notions of fairness, more intuitive than typical group fairness conditions. 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 coincide under some assumptions with causal counterfactual models. Finally, these models make counterfactual approaches to fairness feasible, and we illustrate their practicality and efficiency on fair learning. With this paper, we aim at laying out the theoretical foundations for a new, implementable approach to counterfactual thinking.

Motivation & Objective

• Motivate the need for realistic counterfactuals when causal models are unknown or hard to learn.
• Introduce a transport-based framework that links counterfactuals to joint couplings between observable distributions.
• Show how optimal transport can yield feasible, in-distribution counterfactuals and relate them to causal counterfactuals.
• Develop transport-based counterfactual fairness criteria and demonstrate their use in fair supervised learning.

Proposed method

• Define counterfactual models as collections of joint distributions (couplings) between observable distributions.
• Review Pearl’s causal framework and introduce mass-transportation foundations as a unified viewpoint for counterfactuals.
• Establish connections between optimal transport maps (quadratic cost) and causal counterfactuals under specific assumptions.
• Formulate transport-based counterfactuals as structural counterfactual couplings and relate them to the do-intervention framework.
• Apply the transport-based viewpoint to fairness, recasting counterfactual fairness criteria and proposing causality-free criteria for training fair classifiers.

Experimental results

Research questions

• RQ1 How can transport-based couplings reproduce counterfactual statements without a known causal model?
• RQ2 Under what assumptions do optimal-transport maps recover causal counterfactuals?
• RQ3 How can transport-based counterfactuals be used to define and learn fair classifiers?
• RQ4 What are the practical benefits and limitations of replacing causal models with transport-based surrogates in counterfactual reasoning?

Key findings

• Transport-based counterfactual models provide a feasible, in-distribution alternative to causal counterfactuals.
• Optimal transport maps with quadratic cost can generate the same counterfactual instances as some linear additive causal models under certain assumptions.
• Counterfactual fairness criteria can be reformulated in a transport-based framework, enabling causality-free fair learning.
• The approach yields practical statistical guarantees and supports numerical experiments on fairness datasets.