We consider stochastic settings for clustering, and develop provably-good (approximation) algorithms for a number of these notions. These algorithms allow one to obtain better approximation ratios compared to the usual deterministic clustering setting. Additionally, they offer a number of advantages including providing fairer clustering and clustering which has better long-term behavior for each user. In particular, they ensure that *every user* is guaranteed to get good service (on average). We also complement some of these with impossibility results.
With algorithms increasingly running our world, there has been substantial recent interest on incorporating fairness systematically into algorithms and machine learning. One such notion that has gained importance is that of : in addition to requiring that such as gender or race not be used (explicitly) in decisions, this asks that decisions not be disproportionately different for diverse protected classes @cite_30 . This is developed further in the context of clustering in the work of @cite_13 . Such notions of are considered along with -- treating similar individuals similarly -- in @cite_16 . See @cite_10 for earlier work that developed foundations and connections for several such notions of fairness.
@cite_30 @cite_10 @cite_16 @cite_13
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Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in the data through random projections in a fair'' subspace. We apply this method to densest subgraph and @math -means. For densest subgraph, our approach based on fair projections allows to recover both theoretically and empirically an almost optimal, fair, dense subgraph hidden in the input data. We also show that, under the small set expansion hypothesis, approximating this problem beyond a factor of @math is NP-hard and we show a polynomial time algorithm with a matching approximation bound. We further apply our method to @math -means. In a previous paper, [NIPS 2017] showed that problems such as @math -means can be approximated up to a constant factor while ensuring that none of two protected class (e.g., gender, ethnicity) is disparately impacted. We show that fair projections generalize the concept of fairlet introduced by to any number of protected attributes and improve empirically the quality of the resulting clustering. We also present the first constant-factor approximation for an arbitrary number of protected attributes thus settling an open problem recently addressed in several works. Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study of fair learning under the constraint of differential privacy. We design two learning algorithms that simultaneously promise differential privacy and equalized odds, a 'fairness' condition that corresponds to equalizing false positive and negative rates across protected groups. Our first algorithm is a private implementation of the equalized odds post-processing approach of [, 2016]. This algorithm is appealingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as a form of 'disparate treatment'. Our second algorithm is a differentially private version of the oracle-efficient in-processing approach of [, 2018] that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem. This algorithm is more complex but need not have access to protected group membership at test time. We identify new tradeoffs between fairness, accuracy, and privacy that emerge only when requiring all three properties, and show that these tradeoffs can be milder if group membership may be used at test time. We conclude with a brief experimental evaluation. Algorithms are increasingly used to make important decisions about human lives, ranging from social benefit assignment to predicting risk of criminal recidivism. The sensitivity of these decisions has raised important questions about ensuring fairness in algorithmic decision making. Recent work has focused on addressing two aspects of fairness: distributional fairness, concerning the fairness of the outcomes of decision making, and procedural fairness, concerning the fairness of the decision-making process. Assessment of procedural fairness relies on human judgments, for example, about the fairness of using certain features in the algorithm making the decision. Yet to our knowledge, almost no prior work examines people’s perceptions of fairness in algorithmic decision making. We propose a framework for understanding why people perceive certain features as fair to be used in algorithms. We define a framework of eight underlying properties of features, such as relevance, volitionality and reliability, and hypothesize that people use these properties to form a heuristic for making moral judgments about the fairness of feature use in decision-making algorithms. We evaluate our framework through a series of scenario-based surveys with 576 people. We find that, based on a person’s assessment of the eight underlying properties in our exemplar scenario, we can predict if they will perceive a feature as fair to be used with at least 87 accuracy. New social and economic activities massively exploit big data and machine learning algorithms to do inference on people’s lives. Applications include automatic curricula evaluation, wage determination, and risk assessment for credits and loans. Recently, many governments and institutions have raised concerns about the lack of fairness, equity and ethics in machine learning to treat these problems. It has been shown that not including sensitive features that bias fairness, such as gender or race, is not enough to mitigate the discrimination when other related features are included. Instead, including fairness in the objective function has been shown to be more efficient.