Approximating a RUM from Distributions on k-Slates
This provides a practical solution for modeling user preferences in choice scenarios, though it is incremental as it builds on existing RUM approximation methods.
The authors tackled the problem of fitting Random Utility Models (RUMs) to user choice data from k-sized subsets, developing a polynomial-time algorithm that finds the best average approximation. They achieved this by using a linear program with an approximate separation oracle, which scales effectively to real-world datasets.
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.