Discrimination Patterns — A fine-grained notion to quantify fairness
With the increasing involvement of Machine Learning and AI in our day to day lives, comes the big task of understanding the bias and discrimination that seep into these models through data. To cite a few, racial bias in policing (Mohler et al. 2018), recidivism prediction (Chouldechova 2017), gender bias in hiring (Lahoti et al. 2018), and credit rating (Henderson et al. 2015). The list is endless and is rapidly growing as we continue to integrate AI into more decision making avenues.
Fairness literature has come up with several solutions to limit differential treatment of similar individuals and quantify a classifier’s dicriminatory nature through statistical measures. Some of the prominent approaches include,
- Individual fairness (Dwork et al. 2012; Zemel et al. 2013)
- Disparate Impact and Group Fairness (Feldman et al. 2015; Chouldechova 2017)
- Counterfactual fairness (Kusner et al. 2017)
- Relational fairness (Farnadi, Babaki, and Getoor 2018)
- Equality of opportunity (Hardt et al. 2016)
Most of the explored approaches assume that all feature values are present at prediction time (complete assignment), which is seldom true in a real world scenarios. Such an assumption could miss several instances of biased behaviour that are observed with partial assignment of variables and thus can leave gaps while evaluating models for bias and fairness.
This is the sweet spot where Discrimination Patterns (Choi et al.) comes in. It introduces a new notion of fairness which asks whether the model shows patterns where the decision label for an individual, characterized by (partial) feature observations, changes significantly when one or more sensitive attributes are disclosed.
Degree of Discrimination and Discrimination Pattern
Formally, d being a decision variable, x be an assignment from sensitive attributes and y represents attribute assignment for similar individuals from a group, the degree of discrimination of pattern (xy) is defined as :
The joint assignment of (x,y) forms a Discrimination pattern if
|ΔP,d(x, y)| > δ, where δ is a chosen fairness threshold.
Borrowing from these definitions, we can say that a given model with disctribution P is δ-fair if the model has no discrimination patterns w.r.t δ.
This notion allows us to get a much more fine-grain measure of fairness compared to previous approaches. For example, by definition a discrimination pattern of the form (s,∅) means that |P(d | s) — P(d)| > δ, for some δ, which implies a violation of statistical parity. Hence a δ-fair model guarantees statistical parity but the converse is not true.
In the next article we will talk about how to tractably and quickly find these discrimination patterns to quantify fairness of a probabilistic classifier.
