Certifying the Fairness of KNN in the Presence of Dataset Bias
Yannan Li Jingbo Wang Chao Wang
We propose a method for certifying the fairness of the classification result
of a widely used supervised learning algorithm, the k-nearest neighbors (KNN),
under the assumption that the training data may have historical bias caused by
systematic mislabeling of samples from a protected minority group. To the best
of our knowledge, this is the first certification method for KNN based on three
variants of the fairness definition: individual fairness, $\epsilon$-fairness,
and label-flipping fairness. We first define the fairness certification problem
for KNN and then propose sound approximations of the complex arithmetic
computations used in the state-of-the-art KNN algorithm. This is meant to lift
the computation results from the concrete domain to an abstract domain, to
reduce the computational cost. We show effectiveness of this abstract
interpretation based technique through experimental evaluation on six datasets
widely used in the fairness research literature. We also show that the method
is accurate enough to obtain fairness certifications for a large number of test
inputs, despite the presence of historical bias in the datasets.