The Price of Fair PCA: One Extra Dimension
By Samira Samadi, Uthaipon Tao Tantipongpipat, Jamie H. Morgenstern, Mohit Singh, Santosh Srinivas Vempala. 2018
182 citations recorded by the source corpus.
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.
Subfields: Media Technology, AI Ethics, Fairness & Society
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In Media Technology
In AI Ethics, Fairness & Society
- Aram Galstyan
- Dana Pessach
- Erez Shmueli
- Suresh Venkatasubramanian
- Kristina Lerman
- Fred Morstatter
- Ninareh Mehrabi
- Keith A. Burghardt
Citations in the corpus
- A Survey on Bias and Fairness in Machine Learning (2019, methodology): “In [111] authors show that vanilla PCA can exaggerate the error in reconstruction in one group of people over a different group of equal size, so they propose a fair method to create representations with similar richness for different populations—not to make them indistinguishable, or to hide depend”
- Algorithmic Fairness (2020, background): “More recent mechanisms suggest modifying feature representations, so that a subsequent classifier will be fairer [30, 54, 94, 122, 144].”
- Tilted Empirical Risk Minimization (2020, methodology): “Instead of solving a more complex min-max problem using semi-definite programming as in (Samadi et al., 2018), which scales poorly with problem dimension, we apply gradient-based methods, re-weighting the gradients at each iteration based on the loss on each group.”
- Trustworthy Artificial Intelligence: A Review (2022, methodology): “Decrease F [10, 27, 33, 38, 97, 128, 172] F, P [63, 91, 169, 189] F, A [156]”
- Diversity and Inclusion Metrics in Subset Selection (2020, background): “Geometric or distance-based measures of diversity have also been explored within the sciences, measuring the diversity of a dataset by the dataset’s volume [1, 8, 11, 17, 20, 22, 37], variance as in PCA [30], or other measures of spread.”
- A Review on Fairness in Machine Learning (2022, background): “More recent mechanisms suggest modifying feature representations so that a subsequent classifier will be fairer [38, 74, 139, 180, 218].”
- Fairness in representation: quantifying stereotyping as a representational harm (2019, background): “In the context of unsupervised learning, recent work on fair clustering[12, 31, 3] and PCA[30, 28] seeks to generate a modified representation of the input points so that the new representation (clustering or reduced dimension) satisfies a notion of “balance” with respect to groups.”
- A Geometric Solution to Fair Representations (2020, methodology): “Two methods were instead developed to improve fairness of PCA features [24, 29].”