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.
Abstract. In this paper we study the MapReduce Class (MRC) defined by Karloff et al., 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 Valiant's BSP model of parallel computation and the MPC model of Beame et al.
International audienceWe relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rec-tifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G) 3/2−ǫ . As a corollary, we estab-lish that there exist nondeterministic finite automata (NFAs) with ε-transitions, having n transitions total such that the smallest equivalent ε-free NFA has Ω(n 3/2−ǫ) transitions. We also formulate a version of previous bounds for the weighted set cover problem and discuss its con-nections to giving upper bounds for the possible blow-up
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