Approximating a RUM from Distributions on k-Slates

• URL: http://arxiv.org/abs/2305.13283v1
• Date: Mon, 22 May 2023 17:43:34 GMT
• Title: Approximating a RUM from Distributions on k-Slates
• Authors: Flavio Chierichetti, Mirko Giacchini, Ravi Kumar, Alessandro Panconesi, Andrew Tomkins
• Abstract summary: We find a generalization-time algorithm that finds the RUM that best approximates the given distribution on average. Our theoretical result can also be made practical: we obtain a that is effective and scales to real-world datasets.
• Score: 88.32814292632675
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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