The Price of Fair PCA: One Extra dimension

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Authors

Samira Samadi, Uthaipon Tantipongpipat, Jamie H. Morgenstern, Mohit Singh, Santosh Vempala

Abstract

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher reconstruction error on population A than on B (for example, women versus men or lower- versus higher-educated individuals). This can happen even when the data set has a similar number of samples from A and B. This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A and B. We define the notion of Fair PCA and give a polynomial-time algorithm for finding a low dimensional representation of the data which is nearly-optimal with respect to this measure. Finally, we show on real-world data sets that our algorithm can be used to efficiently generate a fair low dimensional representation of the data.