Jeremy Kun

A Confidence-Based Approach for Balancing Fairness and Accuracy.

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.

Anti-coordination Games and Stable Graph Colorings

Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings exist and when the decision problem is NP-hard. These correspond to finding pure strategy equilibria in the anti-coordination games, whose price of anarchy we also analyze. We further consider the directed case, a generalization that captures both coordination and anti-coordination. We prove the decision problem for non-strict equilibria in directed graphs is NP-hard. Our notions also have multiple connections to other combinatorial questions, and our results resolve some open problems in these areas, most notably the complexity of the strictly unfriendly partition problem.

On the Computational Complexity of MapReduce

In this paper we study the MapReduce Class MRC defined by Karloffi?źeti?źal., which is a formal complexity-theoretic model of MapReduce. We show that constant-round MRC computations can decide regular languages and simulate sublogarithmic space-bounded Turing machines. In addition, we prove hierarchy theorems for MRC under certain complexity-theoretic assumptions. These theorems show that sufficiently increasing the number of rounds or the amount of time per processor strictly increases the computational power of MRC. Our work lays the foundation for further analysis relating MapReduce to established complexity classes. Our results also hold for Valiants BSP model of parallel computation and the MPC model of Beamei?źeti?źal.

Network installation under convex costs

We study the Neighbour-Aided Network Installation Problem (NANIP) introduced previously which asks for a minimal cost ordering of the nodes of a graph, where the cost of visiting a node is a function of the number of its neighbours that have already been visited. This problem has applications in resource management and disaster recovery. In this paper, we analyse the computational hardness of NANIP. In particular we show that this problem is NP-hard even when restricted to convex decreasing cost functions, give a linear approximation lower bound for the greedy algorithm, and prove a general sub-constant approximation lower bound. Then we give a new integer programming formulation of NANIP and empirically observe its speedup over the original integer programme.

Interception in distance-vector routing networks

Despite the large effort devoted to cybersecurity research over the last decades, cyber intrusions and attacks are still increasing. With respect to routing networks, route hijacking has highlighted the need to reexamine the existing protocols that govern traffic routing. In particular, our pri- mary question is how the topology of a network affects the susceptibility of a routing protocol to endogenous route misdirection. In this paper we define and analyze an abstract model of traffic interception (i.e. eavesdropping) in distance-vector routing networks. Specifically, we study al- gorithms that measure the potential of groups of dishonest agents to divert traffic through their infrastructure under the constraint that messages must reach their intended destinations. We relate two variants of our model based on the allowed kinds of lies, define strategies for colluding agents, and prove optimality in special cases. In our main theorem we derive a provably optimal monitoring strategy for subsets of agents in which no two are adjacent, and we extend this strategy to the general case. Finally, we use our results to analyze the susceptibility of real and synthetic networks to endogenous traffic interception. In the Autonomous Systems (AS) graph of the United States, we show that compromising only 18 random nodes in the AS graph surprisingly captures 10% of all traffic paths in the network in expectation when a distance-vector routing protocol is in use.

On Coloring Resilient Graphs

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study

A Boosting Approach to Learning Graph Representations.

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Information Monitoring in Routing Networks.

-resiliently

Locally Boosted Graph Aggregation for Community Detection

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Graphs, New Models, and Complexity

-colorable graphs, which are those