Fair and Diverse DPP-based Data Summarization

Abstract: Sampling methods that choose a subset of the data proportional to its diversity in the feature space are popular for data summarization. However, recent studies have noted the occurrence of bias (under- or over-representation of a certain gender or race) in such data summarization methods. In this paper we initiate a study of the problem of outputting a diverse and fair summary of a given dataset. We work with a well-studied determinantal measure of diversity and corresponding distributions (DPPs) and present a framework that allows us to incorporate a general class of fairness constraints into such distributions. Coming up with efficient algorithms to sample from these constrained determinantal distributions, however, suffers from a complexity barrier and we present a fast sampler that is provably good when the input vectors satisfy a natural property. Our experimental results on a real-world and an image dataset show that the diversity of the samples produced by adding fairness constraints is not too far from the unconstrained case, and we also provide a theoretical explanation of it.