Inferring rankings under constrained sensing

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Inferring rankings under constrained sensing
Motivated by applications like elections, web-page ranking, revenue maximization etc., we consider the question of inferring popular rankings using constrained data. More specifically, we consider the problem of inferring a probability distribution over the group of permutations using its first order marginals. We first prove that it is not possible to recover more than O(n) permutations over n elements with the given information. We then provide a simple and novel algorithm that can recover up to O(n) permutations under a natural stochastic model; in this sense, the algorithm is optimal. In certain applications, the interest is in recovering only the most popular (or mode) ranking. As a second result, we provide an algorithm based on the Fourier Transform over the symmetric group to recover the mode under a natural majority condition; the algorithm turns out to be a maximum weight matching on an appropriately defined weighted bipartite graph. The questions considered are also themati...
Srikanth Jagabathula, Devavrat Shah
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Srikanth Jagabathula, Devavrat Shah
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