Extending Fair Null-Space Projections for Continuous Attributes to Kernel Methods

With the on-going integration of machine learning systems into the everyday social life of millions the notion of fairness becomes an ever increasing priority in their development. Fairness notions commonly rely on protected attributes to assess potential biases. Here, the majority of literature focuses on discrete setups regarding both target and protected attributes. The literature on continuous attributes especially in conjunction with regression - we refer to this as continuous fairness - is scarce. A common strategy is iterative null-space projection which as of now has only been explored for linear models or embeddings such as obtained by a non-linear encoder. We improve on this by extending this to kernel induced feature spaces by means of the ``empirical feature space''. We theoretically derive this as a direct transformation of the kernel matrix yielding a model and fairness-score agnostic method applicable to continuous protected attributes. We demonstrate that our novel approach in conjunction with Support Vector Regression (SVR) provides competitive or improved performance across multiple datasets in comparison to other contemporary methods.

Machine Learning models are trained on data which may reflect existing unfairness in society. Take age as an example: we consider two people with similar qualification; one is hired while the other is not because they are much younger. We consider this decision "unfair'' as it is based on a factor (age) - so-called "protected attribute'' - that should not be relevant for the actual decision. "Kernel methods'' are a large class of well established Machine Learning models that are particularly effective for small data. There are some approaches to make kernel methods "fair'', but those usually expect the protected attributes to form categories, e.g., "old" vs "young". But does a 45 year old person count as young or old? We overcome this limitation by allowing numerical values. An existing work aims to remove information about the protected attribute from the data but is limited to remove simple (``linear'') relations. As "kernel methods'' implicitly finds complex - "non-linear'' -- features they are able to recover previously removed information. This work provides means to perform this method in a way to directly affect these "non-linear features'' - still yielding useful, but (in the above interpretation of "fair'') fairer decisions.