Machine learning has grown in popularity to help assign resources and make decisions about users, which can result in discrimination. This includes hiring markets, where employers have increasingly been interested in using automated tools to help hire candidates. In response, there has been significant effort in attempting to understand and mitigate the sources of discrimination in these tools. However, previous work has largely assumed that discrimination is the result of some initial unequal distribution of resources across groups: one group is on average less qualified, there is less training data for one group, or the classifier is less accurate on one group, etc. Recent work on relational equality have suggested that there are other sources of discrimination that are non-distributional, namely inequality in social relationships. Here, we demonstrate how discrimination can arise from a non-distributional source: We provide subgame perfect equilibria in a simple sequential model of a hiring market with Rubinstein-style bargaining between firms and candidates that exhibits discriminatory outcomes, yet there was no initial unequal distribution of resources across groups of candidates or firms. We provide the range of possible expected payoffs to the firms and candidates at equilibrium, including asymmetric payoffs where some candidates receive less. This is the result of asymmetric strategies where firms successfully take advantage of those candidates, resulting in discrimination. Thus, we show that we must look beyond the distribution of resources to understand sources of discrimination in machine learning.

Graph Neural Network (GNN) research has highlighted a relationship between high homophily (i.e., the tendency of nodes of the same class to connect) and strong predictive performance in node classification. However, recent work has found the relationship to be more nuanced, demonstrating that simple GNNs can learn in certain heterophilous settings. To resolve these conflicting findings and align closer to real-world datasets, we go beyond the assumption of a global graph homophily level and study the performance of GNNs when the local homophily level of a node deviates from the global homophily level. Through theoretical and empirical analysis, we systematically demonstrate how shifts in local homophily can introduce performance degradation, leading to performance discrepancies across local homophily levels. We ground the practical implications of this work through granular analysis on five real-world datasets with varying global homophily levels, demonstrating that (a) GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, and (b) high local homophily does not necessarily confer high performance for a node. We further show that GNNs designed for globally heterophilous graphs can alleviate performance discrepancy by improving performance across local homophily levels, offering a new perspective on how these GNNs achieve stronger global performance.

Existing efforts to formulate computational definitions of fairness have largely focused on distributional notions of equality, defined through how resources or decisions are divided. Yet existing discrimination is often the result of unequal social relations, rather than simply an unequal distribution of resources. We show how optimizing for existing computational definitions of fairness fails to prevent unequal social relations by providing an example of a self-confirming equilibrium in a simple hiring market that is relationally unequal but satisfies existing distributional notions of fairness. We introduce a notion of blatant relational unfairness for complete-information games, and discuss how this definition helps initiate a new approach to incorporating relational equality into computational systems.

Navigating the ethical and societal impacts of technologies.

Algorithms and other formal models purportedly incorporating human values like fairness have grown increasingly popular in computer science. In response to sociotechnical challenges in the use of these models, designers and researchers have taken widely divergent positions on how formal models incorporating aspects of human values should be used: encouraging their use, moving away from them, or ignoring the normative consequences altogether. In this paper, we seek to resolve these divergent positions by identifying the main conceptual limits of formal modeling, and develop four reflexive values--value fidelity, appropriate accuracy, value legibility, and value contestation--vital for incorporating human values adequately into formal models. We then provide a brief methodology for reflexively designing formal models incorporating human values.

In the problem of learning a class ratio from unlabeled data, which we call CR learning, the training data is unlabeled, and only the ratios, or proportions, of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of CR learning and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently CR learned is a strict subset of what can be learned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose CR learnability is independent of ZFC, the standard set theoretic axioms. This implies that CR learning cannot be easily characterized (like PAC by VC dimension).

Recent work has documented instances of unfairness in deployed machine learning models, and significant researcher effort has been dedicated to creating algorithms that intrinsically consider fairness. In this work, we highlight another source of unfairness: market forces that drive differential investment in the data pipeline for differing groups. We develop a high-level model to study this question. First, we show that our model predicts unfairness in a monopoly setting. Then, we show that under all but the most extreme models, competition does not eliminate this tendency, and may even exacerbate it. Finally, we consider two avenues for regulating a machine-learning driven monopolist - relative error inequality and absolute error-bounds - and quantify the price of fairness (and who pays it). These models imply that mitigating fairness concerns may require policy-driven solutions, not only technological ones.

Recent debate within the FAT* community has focused on how the field conceptualizes the problems it seeks to address, what approach the field should take in attempting to address these problems, and whether the field should even pursue some of the proposed remedies. Questions regarding when not to design, build, or deploy a technology are perhaps the most common expression of this trend. Identifying the problems to address is inextricably linked to the broader question of how to collectively make decisions about what technologies our societies need and want.

In this work, we study how to use sampling to speed up mechanisms for answering adaptive queries into datasets without reducing the accuracy of those mechanisms. This is important to do when both the datasets and the number of queries asked are very large. In particular, we describe a mechanism that provides a polynomial speed-up per query over previous mechanisms, without needing to increase the total amount of data required to maintain the same generalization error as before. We prove that this speed-up holds for arbitrary statistical queries. We also provide an even faster method for achieving statistically-meaningful responses wherein the mechanism is only allowed to see a constant number of samples from the data per query. Finally, we show that our general results yield a simple, fast, and unified approach for adaptively optimizing convex and strongly convex functions over a dataset.

The study of influence maximization in social networks has largely ignored disparate effects these algorithms might have on the individuals contained in the social network. Individuals may place a high value on receiving information, e.g. job openings or advertisements for loans. While well-connected individuals at the center of the network are likely to receive the information that is being distributed through the network, poorly connected individuals are systematically less likely to receive the information, producing a gap in access to the information between individuals. In this work, we study how best to spread information in a social network while minimizing this access gap. We propose to use the maximin social welfare function as an objective function, where we maximize the minimum probability of receiving the information under an intervention. We prove that in this setting this welfare function constrains the access gap whereas maximizing the expected number of nodes reached does not. We also investigate the difficulties of using the maximin, and present hardness results and analysis for standard greedy strategies. Finally, we investigate practical ways of optimizing for the maximin, and give empirical evidence that a simple greedy-based strategy works well in practice.

In this work, we study how to use sampling to speed up mechanisms for answering adaptive queries into datasets without reducing the accuracy of those mechanisms. This is important to do when both the datasets and the number of queries asked are very large. In particular, we describe a mechanism that provides a polynomial speed-up per query over previous mechanisms, without needing to increase the total amount of data required to maintain the same generalization error as before. We prove that this speed-up holds for arbitrary statistical queries. We also provide an even faster method for achieving statistically-meaningful responses wherein the mechanism is only allowed to see a constant number of samples from the data per query. Finally, we show that our general results yield a simple, fast, and unified approach for adaptively optimizing convex and strongly convex functions over a dataset.

Learning automata is a foundational problem in computational learning theory. However, even efficiently learning random DFAs is hard. A natural restriction of this problem is to consider learning random DFAs under the uniform distribution. To date, this problem has no non-trivial lower bounds nor algorithms faster than brute force. In this note, we propose a method to find faster algorithms for this problem. We reduce the learning problem to a conjecture about meeting times of random walks over random DFAs, which may be of independent interest to prove.

The central aim of most fields of data analysis and experimental scientific investigation is to draw valid conclusions from a given data set. But when past inferences guide future inquiries into the same dataset, reaching valid inferences becomes significantly more difficult. In addition to avoiding the overfitting that can result from adaptive analysis, a data analyst often wants to use as little time and data as possible. A recent line of work in the theory community has established mechanisms that provide low generalization error on adaptive queries, yet there remain large gaps between established theoretical results and how data analysis is done in practice. Many practitioners, for instance, successfully employ bootstrapping and related sampling approaches in order to maintain validity and speed up analysis, but prior to this work, no theoretical analysis existed to justify employing such techniques in this adaptive setting. In this paper, we show how these techniques can be used to provably guarantee validity while speeding up analysis. Through this investigation, we initiate the study of sub-linear time mechanisms to answer adaptive queries into datasets. Perhaps surprisingly, we describe mechanisms that provide an exponential speed-up per query over previous mechanisms, without needing to increase the total amount of data needed for low generalization error. We also provide a method for achieving statistically-meaningful responses even when the mechanism is only allowed to see a constant number of samples from the data per query.

For any stream of time-stamped edges that form a dynamic network, an important choice is the aggregation granularity that an analyst uses to bin the data. Picking such a windowing of the data is often done by hand, or left up to the technology that is collecting the data. However, the choice can make a big difference in the properties of the dynamic network. This is the time scale detection problem. In previous work, this problem is often solved with a heuristic as an unsupervised task. As an unsupervised problem, it is difficult to measure how well a given algorithm performs. In addition, we show that the quality of the windowing is dependent on which task an analyst wants to perform on the network after windowing. Therefore the time scale detection problem should not be handled independently from the rest of the analysis of the network. We introduce a framework that tackles both of these issues: By measuring the performance of the time scale detection algorithm based on how well a given task is accomplished on the resulting network, we are for the first time able to directly compare different time scale detection algorithms to each other. Using this framework, we introduce time scale detection algorithms that take a supervised approach: they leverage ground truth on training data to find a good windowing of the test data. We compare the supervised approach to previous approaches and several baselines on real data.

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of LLP and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently LLP learned is a strict subset of what can be leaned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose learnability in LLP is independent of ZFC, the standard set theoretic axioms. This implies that LLP learning cannot be easily characterized (like PAC by VC dimension).

Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The k-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most k. The sequence of k-betweenness centralities for all possible values of k forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees. We show that for scale-free random trees, for fixed k, the expectation of k-betweenness centrality strictly decreases as the index of the vertex increases. We also analyze worst-case properties of profiles in terms of the distance of profiles from being monotone, and the number of times pairs of profiles can cross. This is related to whether k-betweenness centrality, for small values of k, may be used instead of having to consider all shortest paths. Bounds are given that are optimal in order of magnitude. We also present some experimental results for scale-free random trees.

We study three classical machine learning algorithms in the context of algorithmic fairness: adaptive boosting, support vector machines, and logistic regression. Our goal is to maintain the high accuracy of these learning algorithms while reducing the degree to which they discriminate against individuals because of their membership in a protected group.Our first contribution is a method for achieving fairness by shifting the decision boundary for the protected group. The method is based on the theory of margins for boosting. Our method performs comparably to or outperforms previous algorithms in the fairness literature in terms of accuracy and low discrimination, while simultaneously allowing for a fast and transparent quantification of the trade-off between bias and error.Our second contribution addresses the shortcomings of the bias-error trade-off studied in most of the algorithmic fairness literature. We demonstrate that even hopelessly naive modifications of a biased algorithm, which cannot be reasonably said to be fair, can still achieve low bias and high accuracy. To help to distinguish between these naive algorithms and more sensible algorithms we propose a new measure of fairness, called resilience to random bias (RRB). We demonstrate that RRB distinguishes well between our naive and sensible fairness algorithms. RRB together with bias and accuracy provides a more complete picture of the fairness of an algorithm.

We investigate how to reconstruct social networks from voting data. In particular, given a voting model that considers social network structure, we aim to find the network that best explains the agents' votes. We study two plausible voting models, one edge-centric and the other vertex-centric.For these models, we give algorithms and lower bounds, characterizing cases where network recovery is possible and where it is computationally difficult. We also test our algorithms on United States Senate data.Despite the similarity of the two models, we show that their respective network recovery problems differ in complexity and involve distinct algorithmic challenges. Moreover, the networks produced when working under these models can also differ significantly. These results indicate that great care should be exercised when choosing a voting model for network recovery tasks.

Oversampling is a common characteristic of data representing dynamic networks. It introduces noise into representations of dynamic networks, but there has been little work so far to compensate for it. Oversampling can affect the quality of many important algorithmic problems on dynamic networks, including link prediction. Link prediction seeks to predict edges that will be added to the network given previous snapshots. We show that not only does oversampling affect the quality of link prediction, but that we can use link prediction to recover from the effects of oversampling. We also introduce a novel generative model of noise in dynamic networks that represents oversampling. We demonstrate the results of our approach on both synthetic and real-world data.

In this paper we study MapReduce computations from a complexity-theoretic perspective. First, we formulate a uniform version of the MRC model of Karloff et al. (2010). We then show that the class of regular languages, and moreover all of sublogarithmic space, lies in constant round MRC. This result also applies to the MPC model of Andoni et al. (2014). In addition, we prove that, conditioned on a variant of the Exponential Time Hypothesis, there are strict hierarchies within MRC so that increasing the number of rounds or the amount of time per processor increases the power of MRC. To the best of our knowledge we are the first to approach the MapReduce model with complexity-theoretic techniques, and our work lays the foundation for further analysis relating MapReduce to established complexity classes.