Diagonals of Doubly Stochastic Matrices

Marcus, Michel; Ree, Rimhak

doi:10.1093/qmath/10.1.296

Cited by 48 publications

(18 citation statements)

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“…Request permissions from permissions@acm.org. KDD '18, August [19][20][21][22][23]2018, London, United Kingdom © 2018 Copyright held by the owner/author(s). Publication rights licensed to Association for Computing Machinery.…”

Section: Introductionmentioning

confidence: 99%

Fairness of Exposure in Rankings

Singh

Joachims

2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

454

544

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Rankings are ubiquitous in the online world today. As we have transitioned from finding books in libraries to ranking products, jobs, job applicants, opinions and potential romantic partners, there is a substantial precedent that ranking systems have a responsibility not only to their users but also to the items being ranked. To address these often conflicting responsibilities, we propose a conceptual and computational framework that allows the formulation of fairness constraints on rankings in terms of exposure allocation. As part of this framework, we develop efficient algorithms for finding rankings that maximize the utility for the user while provably satisfying a specifiable notion of fairness. Since fairness goals can be application specific, we show how a broad range of fairness constraints can be implemented using our framework, including forms of demographic parity, disparate treatment, and disparate impact constraints. We illustrate the effect of these constraints by providing empirical results on two ranking problems. CCS CONCEPTS• Information systems → Probabilistic retrieval models; Retrieval effectiveness; Presentation of retrieval results; KEYWORDS fairness in rankings; fairness; algorithmic bias; position bias; equal opportunity ACM Reference Format:

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Section: Introductionmentioning

confidence: 99%

Fairness of Exposure in Rankings

Singh

Joachims

2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

454

544

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“…It was shown by Marcus and Ree [30] (see also [31]) via the Minkowski -Carathéodory theorem that every bistochastic matrix is a convex combination of at most ðn 2 1Þ 2 þ 1 permutation matrices. The Birkhoff polytope should not be confused with the permutahedron.…”

Section: Random Bistochastic Matricesmentioning

confidence: 99%

Aspects of large random Markov kernels

Chafäı

2009

Stochastics

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We briefly review certain asymptotic properties of random Markov kernels on a finite state space. These models can be thought of as finite Markov chains in random environment. Here, the asymptotics are taken with respect to the cardinality of the state space. We study, for instance, the behaviour of the normalized invariant vector, the global behaviour of the spectrum and the extremal eigenvalues. The analysis of these models involves Random Matrix Theory, convex compact polytopes and finite graphs with random weights. We also give some open problems related to these models.

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“…Thus an nXn matrix S = [s t j] belongs to Cl n provided s t]f > 0 (i, j = 1,..., n), and the sum of the entries in each row and in each column of S equals one. It is readily verified that il n is a convex polytope in Euclidean n 2 -space, and it was shown in [8] that fl n has dimension n 2 -2n +1. Birkhoff [1; 10,p.…”

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confidence: 93%