Transport-based Counterfactual Models
  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.
