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.

翻译：本文研究如何将随机效用模型（RUM）拟合到用户选择的问题。给定一个全集所有大小为$k$的子集的胜出分布，我们提出一个多项式时间算法，用于找到在平均意义上最优近似该给定分布的RUM。该算法基于一个线性规划，我们通过椭球法对其进行求解。鉴于其对应的分离判定问题为NP困难，我们设计了一种近似分离判定方法，该方法可视为加权反馈弧集问题在图论中的超图推广。我们的理论结果同样具有实际应用价值：我们获得了一种启发式算法，该算法在真实数据集上表现高效且可扩展。