  Machine learning algorithms can produce biased outcome/prediction, typically,
against minorities and under-represented sub-populations. Therefore, fairness
is emerging as an important requirement for the large scale application of
machine learning based technologies. The most commonly used fairness notions
(e.g. statistical parity, equalized odds, predictive parity, etc.) are
observational and rely on mere correlation between variables. These notions
fail to identify bias in case of statistical anomalies such as Simpson's or
Berkson's paradoxes. Causality-based fairness notions (e.g. counterfactual
fairness, no-proxy discrimination, etc.) are immune to such anomalies and hence
more reliable to assess fairness. The problem of causality-based fairness
notions, however, is that they are defined in terms of quantities (e.g. causal,
counterfactual, and path-specific effects) that are not always measurable. This
is known as the identifiability problem and is the topic of a large body of
work in the causal inference literature. This paper is a compilation of the
major identifiability results which are of particular relevance for machine
learning fairness. The results are illustrated using a large number of examples
and causal graphs. The paper would be of particular interest to fairness
researchers, practitioners, and policy makers who are considering the use of
causality-based fairness notions as it summarizes and illustrates the major
identifiability results
