[Paper Review] PC-Fairness: A Unified Framework for Measuring Causality-based Fairness

Yongkai Wu, Lu Zhang+2 more|arXiv (Cornell University)|Oct 20, 2019

Ethics and Social Impacts of AI42 citations

TL;DR

The paper proposes PC fairness, a unified, path-specific counterfactual fairness framework, and a linear programming method to bound PC fairness under unidentifiable causal scenarios driven by response-function variables.

ABSTRACT

A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions is identifiability, i.e., whether they can be uniquely measured from observational data, which is a critical barrier to applying these notions to real-world situations. In this paper, we develop a framework for measuring different causality-based fairness. We propose a unified definition that covers most of previous causality-based fairness notions, namely the path-specific counterfactual fairness (PC fairness). Based on that, we propose a general method in the form of a constrained optimization problem for bounding the path-specific counterfactual fairness under all unidentifiable situations. Experiments on synthetic and real-world datasets show the correctness and effectiveness of our method.

Motivation & Objective

• Propose a unified definition of path-specific counterfactual fairness (PC fairness) that covers existing causality-based fairness notions.
• Represent all causal effects via path-specific counterfactual effects to enable broad applicability.
• Address identifiability by bounding PC fairness in unidentifiable situations using a constrained optimization approach.
• Develop a framework that allows hidden confounders and arbitrary data-generating processes while assuming a given causal graph.

Proposed method

• Introduce path-specific counterfactual effects and PC fairness formalism.
• Parameterize causal models with response-function variables to capture all randomness and traverse possible models.
• Express observational distributions and path-specific counterfactual quantities as linear functions of the response-function distribution.
• Formulate a linear programming problem to minimize or maximize PC fairness bounds subject to observational constraints.
• Provide tight bounds on PC fairness by solving the constrained optimization problem under various unidentifiable graph structures.

Experimental results

Research questions

• RQ1 How can PC fairness subsume and unify existing causality-based fairness notions?
• RQ2 How can we bound path-specific counterfactual fairness in the presence of unidentifiability?
• RQ3 Do response-function based parameterizations yield tight, tractable bounds for PC fairness across different graph structures?
• RQ4 Can the framework accommodate hidden confounders and general data-generating processes without biasing results?

Key findings

• PC fairness can represent most previous causality-based fairness notions as special cases.
• A constrained optimization approach yields tight, unique bounds on path-specific counterfactual fairness under unidentifiable conditions.
• The response-function variable formalism enables explicit traversal of all compatible causal models to derive bounds.
• Experiments on synthetic and real-world data show the method bounds PC fairness correctly and can outperform prior bounding methods in tightness.
• The framework remains valid without assuming independence of hidden confounders or linearity in the data-generating process.