Approximating a RUM from Distributions on k-Slates
Flavio Chierichetti Mirko Giacchini Ravi Kumar Alessandro Panconesi Andrew Tomkins
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.