  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.
