Approximating a RUM from Distributions on k-Slates
Machine Learning
2023-05-23 v1 Data Structures and Algorithms
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 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.
Cite
@article{arxiv.2305.13283,
title = {Approximating a RUM from Distributions on k-Slates},
author = {Flavio Chierichetti and Mirko Giacchini and Ravi Kumar and Alessandro Panconesi and Andrew Tomkins},
journal= {arXiv preprint arXiv:2305.13283},
year = {2023}
}