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

<p>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.</p>