Fair and Diverse DPP-Based Data Summarization

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 {–} e.g., under or over representation of a particular gender or ethnicity {–} 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. Designing efficient algorithms to sample from these constrained determinantal distributions, however, suffers from a complexity barrier; we present a fast sampler that is provably good when the input vectors satisfy a natural property. Our empirical results on both real-world and synthetic datasets show that the diversity of the samples produced by adding fairness constraints is not too far from the unconstrained case.