Extending Decision Tree to Handle Multiple Fairness Criteria

1 Introduction

AI-based decision systems interact with humans in many domains of application, and in some cases have replaced them. AI has spread widely because it is a powerful tool for making optimised decisions based on massive amounts of structured and unstructured data. However, the understanding and adoption of AI depends on criteria such as transparency, explainability and fairness. Explainable AI (XAI) is an immense help to companies in terms of producing AI systems that are trustworthy. However, XAI alone does not solve all of the possible ethics-related issues. AI systems are vulnerable to biases in the data that might render their decisions "unfair" to certain population subgroups based on gender or race. The different preferences and outlooks in different cultures involve different ways of looking at fairness, which makes it harder to come up with a single definition that is acceptable to everyone in a given situation.

Table 1 summarises three families of observational 1 fairness criteria typically adopted (for details see [Barocas et al., 2017]), where Y , ˆ Y and S are the target variable, the model outcome and the sensitive attribute, respectively.

1 A criteria is called "observational" if by knowing the joint distribution ( ˆ Y , S, Y ) is possible determine its value without ambiguity.

As detailed in [Zafar et al., 2019], the mitigation strategies proposed in prior studies typically lack flexibility with respect to one or more of the following aspects: (i) They are specifically designed for only one fairness criterion, and as a consequence cannot accommodate more than one simultaneously; (ii) they cannot ensure fairness with respect to multiple sensitive features simultaneously; (iii) the proper mitigation model depends on the chosen definition of fairness; (iv) they are designed as a black box, i.e. they are not directly interpretable. To overcome these limitations we are developing FFTree, a new transparent, flexible and fairness-aware classifier.

2 RelatedWorks

Our work is related to the discrimination-aware decision tree, which is an intersection between fairness and interpretability in supervised machine learning. A decision tree classifier [Brieman et al., ] is one of the most popular algorithms in machine learning given its intelligibility. In a discriminationaware decision tree, fairness criteria are taken into consideration with the performance optimisation in the evaluation at each internal node. The first "fair-tree" was introduced in [Kamiran et al., 2010], while the authors of [Zhang and Ntoutsi, 2019] have proposed important developments. All of these works handle the trade-off between accuracy and fairness by combining performance and fairness criteria through an operation, such as addition or multiplication. However, the different metrics could be incomparable. Moreover, they permit to mitigate a limited number of fairness criterion.

3 Contribution

We present FFTree, a new transparent, flexible and fairnessaware classifier. As a novelty, FFTree enchances the classical approach introduced in [Brieman et al., ] with a new approach to find a "fair" split to: (i) satisfy a fairness constraint selected from a wide range of possible definitions of fairness; (ii) provide more than one fairness formalisation simultaneously (when this is algebraically possible); (iii) handle more than one sensitive attributes at the same time; and (iv) set the required level of fairness as an input parameter to meet different business needs or regulatory requirements. FFTree can support users in many different application domains, including promoting gender equality and reducing inequalities within ethnic groups.

4 How FFTreeWorks

Given the domain dom(Xi) of the input features X = Xi, i = 1, .., n and the target label Y , the goal of a splitting criterion is to find a rule to separate a node D into "purer" branches Dj. The concept of purity is related to the target label Y , whereas the splitting criterion is determined by iteratively observing the variables X and their domains. Formally, an increase in purity is called Information gain (IG), and can be expressed as the differences in the entropy H of Y between the node and the average for the branches created by the splitting criterion a:

Among all the splitting criterion under consideration, the one that locally (at the node) optimises the IG is chosen. In our approach, the best splitting criterion is the one that locally optimizes the IG, from among the options that satisfy the imposed fairness constraints FC.

Where FC is a fairness constraint, S is a binary sensitive attribute and δ is the maximum level of discrimination locally permitted. Currently, FFTree allows the users to choose FC among the observational fairness criteria summarized in Table 1, expressed as the absolute value of the difference between the two probability terms. FFTree permits to choose more than one fairness metric and more than one sensitive attribute S. All the selected criteria must be satisfied by each split; if no solutions are found the node becomes a leaf. To calculate the fairness metrics we compute the local prediction ˆ Y of each split assigning a value of one to the branch with the higher percentage of Y and zero to the other branch.

Demo. FFTree demonstration, using the open dataset Adult, is available at tinyurl.com/DemoFFTree.

4.1 Properties and Limitations

Properties. When FFTree is trained to provide perfect independence in each local branch (δ = 0), the resulting global tree is fairness-pruning-invariant and fairnessthreshold-invariant, since by pruning FFTree or changing the classification threshold, the output continues to provide perfect independence. Moreover, the optimisation at local level implies that all the rules shown by FFTree are consistent with the chosen fairness constraint, while other fair trees, optimised at global level, could be composed of a series of rules which, if taken individually, could be unfair. We suggest to tune the δ hyperparameter to identify at the global level the best performance-fairness trade-off for the application domain.

Limitations. Meeting different fairness criteria at the same time is not always possible. These criteria constrain the joint distribution in non-trivial ways. We should therefore suspect that imposing any two of them simultaneously will overconstrain the space to the point where only degenerate solutions remain. Moreover, under certain assumptions, different fairness criteria become mutually exclusive (see [Barocas et al., 2017]).

5 Experiments and Future Directions

We evaluate FFTree on both (i) a well-known benchmark dataset from the literature, and (ii) a real-world private dataset owned by Intesa Sanpaolo containing about 250,000 records related to the granting of personal loans. We prove that FFTree is competitive with state-of-the-art fair trees in the common features, and thanks to its novel functionality, it can support users in very different application domains.

To make a more relevant contribution to the field of discrimination-aware data mining, we intend to release the code as open source, to allow the community to utilise it and improve it. A natural evolution of FFTree would be the addition of new fairness criteria or different formalisation of the current criteria. To improve performance, we are currently studying how to use FFTree for tree-based machine learning algorithms, such as Random Forest. FFTree can also be used in place of classic decision trees in XAI tools that act on surrogates such as ContrXT [Malandri et al., 2022] or to monitor fairness through time [Castelnovo et al., 2021].

Acknowledgements

Andrea Cosentini, Lorenzo Malandri, Fabio Mercorio and Mario Mezzanzanica contributed to this work. This research was supported by the outstanding Fairness team of the Data Science & AI Office at Intesa Sanpaolo.