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Register a new userFair and Useful Cohort Selection
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Added by
Huy Nguyen
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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As important decisions about the distribution of societys resources become increasingly automated, it is essential to consider the measurement and enforcement of fairness in these decisions. In this work we build on the results of Dwork and Ilvento ITCS19, which laid the foundations for the study of fair algorithms under composition. In particular, we study the cohort selection problem, where we wish to use a fair classifier to select $k$ candidates from an arbitrarily ordered set of size $n>k$, while preserving individual fairness and maximizing utility. We define a linear utility function to measure performance relative to the behavior of the original classifier. We develop a fair, utility-optimal $O(n)$-time cohort selection algorithm for the offline setting, and our primary result, a solution to the problem in the streaming setting that keeps no more than $O(k)$ pending candidates at all time.
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We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and requires exponential complexity to solve (i.e., intractable); we formulate a weaker version of this NP-hard problem, where the goal is to find a locally optimal solution. We show that our proposed algorithms can find a locally optimal solution in near linear time. Our algorithms require neither positive nor integer elements in the input set, hence, they are more widely applicable.
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We present an $(e^{O(p)} frac{log ell}{loglogell})$-approximation algorithm for socially fair clustering with the $ell_p$-objective. In this problem, we are given a set of points in a metric space. Each point belongs to one (or several) of $ell$ groups. The goal is to find a $k$-medians, $k$-means, or, more generally, $ell_p$-clustering that is simultaneously good for all of the groups. More precisely, we need to find a set of $k$ centers $C$ so as to minimize the maximum over all groups $j$ of $sum_{u text{ in group }j} d(u,C)^p$. The socially fair clustering problem was independently proposed by Ghadiri, Samadi, and Vempala [2021] and Abbasi, Bhaskara, and Venkatasubramanian [2021]. Our algorithm improves and generalizes their $O(ell)$-approximation algorithms for the problem. The natural LP relaxation for the problem has an integrality gap of $Omega(ell)$. In order to obtain our result, we introduce a strengthened LP relaxation and show that it has an integrality gap of $Theta(frac{log ell}{loglogell})$ for a fixed $p$. Additionally, we present a bicriteria approximation algorithm, which generalizes the bicriteria approximation of Abbasi et al. [2021].
Graph cut problems form a fundamental problem type in combinatorial optimization, and are a central object of study in both theory and practice. In addition, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed in a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different definitions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem modeling disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.
We study fair clustering problems as proposed by Chierichetti et al. (NIPS 2017). Here, points have a sensitive attribute and all clusters in the solution are required to be balanced with respect to it (to counteract any form of data-inherent bias). Previous algorithms for fair clustering do not scale well. We show how to model and compute so-called coresets for fair clustering problems, which can be used to significantly reduce the input data size. We prove that the coresets are composable and show how to compute them in a streaming setting. Furthermore, we propose a variant of Lloyds algorithm that computes fair clusterings and extend it to a fair k-means++ clustering algorithm. We implement these algorithms and provide empirical evidence that the combination of our approximation algorithms and the coreset construction yields a scalable algorithm for fair k-means clustering.
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