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Approximating a RUM from Distributions on k-Slates

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arxiv 2305.13283 v1 pith:Z6P72VZ4 submitted 2023-05-22 cs.LG cs.DS

Flavio Chierichetti , Mirko Giacchini , Ravi Kumar , Alessandro Panconesi , Andrew Tomkins This is my paper · ORCID
classification cs.LGcs.DS
keywords givenproblemalgorithmdistributionsobtainoracleseparationapproximate
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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 corresponding 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 is effective and scales to real-world datasets.

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Cited by 3 Pith papers

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