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arXiv · 2305.13283

Approximating a RUM from Distributions on k-Slates

Flavio Chierichetti·Mirko Giacchini·Ravi Kumar·Alessandro Panconesi·Andrew Tomkins
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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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Flavio Chierichetti, Mirko Giacchini, Ravi Kumar, Alessandro Panconesi, Andrew Tomkins. 2023-05-22. Approximating a RUM from Distributions on k-Slates. https://arxiv.org/abs/2305.13283

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