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Approximating a RUM from Distributions on $k$-Slates

Flavio Chierichetti · Mirko Giacchini · Ravi Kumar · Alessandro Panconesi · Andrew Tomkins

Auditorium 1 Foyer 106

Abstract: In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best approximates the given distribution on average. Our algorithm is based on a linear program that we solve using the ellipsoid method. Given that its separation oracle problem is NP-hard, we devise an approximate separation oracle that can be viewed as a generalization of the weighted Feedback Arc Set problem to hypergraphs. Our theoretical result can also be made practical: we obtain a heuristic that scales to real-world datasets.

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