Guangya Cai

Guangya Cai

Selecting a subset of the $k$ "best" items from a dataset of $n$ items, based on a scoring function, is a key task in decision-making. Given the rise of automated decision-making software, it is important that the outcome of this process, called top-$k$ selection, is fair. Here we consider the problem of identifying a fair linear scoring function for top-$k$ selection. The function computes a score for each item as a weighted sum of its (numerical) attribute values, and must ensure that the selected subset includes adequate representation of a minority or historically disadvantaged group. Existing algorithms do not scale efficiently, particularly in higher dimensions. Our hardness analysis shows that in more than two dimensions, no algorithm is likely to achieve good scalability with respect to dataset size, and the computational complexity is likely to increase rapidly with dimensionality. However, the hardness results also provide key insights guiding algorithm design, leading to our two-pronged solution: (1) For small values of $k$, our hardness analysis reveals a gap in the hardness barrier. By addressing various engineering challenges, including achieving efficient parallelism, we turn this potential of efficiency into an optimized algorithm delivering substantial practical performance gains. (2) For large values of $k$, where the hardness is robust, we employ a practically efficient algorithm which, despite being theoretically worse, achieves superior real-world performance. Experimental evaluations on real-world datasets then explore scenarios where worst-case behavior does not manifest, identifying areas critical to practical performance. Our solution achieves speed-ups of up to several orders of magnitude compared to SOTA, an efficiency made possible through a tight integration of hardness analysis, algorithm design, practical engineering, and empirical evaluation.

Guangya Cai

Fair top-$k$ selection, which ensures appropriate proportional representation of members from minority or historically disadvantaged groups among the top-$k$ selected candidates, has drawn significant attention. We study the problem of finding a fair (linear) scoring function with multiple protected groups while also minimizing the disparity from a reference scoring function. This generalizes the prior setup, which was restricted to the single-group setting without disparity minimization. Previous studies imply that the number of protected groups may have a limited impact on the runtime efficiency. However, driven by the need for experimental exploration, we find that this implication overlooks a critical issue that may affect the fairness of the outcome. Once this issue is properly considered, our hardness analysis shows that the problem may become computationally intractable even for a two-dimensional dataset and small values of $k$. However, our analysis also reveals a gap in the hardness barrier, enabling us to recover the efficiency for the case of small $k$ when the number of protected groups is sufficiently small. Furthermore, beyond measuring disparity as the "distance" between the fair and the reference scoring functions, we introduce an alternative disparity measure$\unicode{x2014}$utility loss$\unicode{x2014}$that may yield a more stable scoring function under small weight perturbations. Through careful engineering trade-offs that balance implementation complexity, robustness, and performance, our augmented two-pronged solution demonstrates strong empirical performance on real-world datasets, with experimental observations also informing algorithm design and implementation decisions.