论文标题
在（排名）选择的绿色摩尔鞋类型模型上
On A Mallows-type Model For (Ranked) Choices
论文作者
论文摘要
我们考虑一个偏好学习设置，每个参与者都会在显示的一组候选人中选择$ k $最喜欢的物品的有序列表。 （对于每个参与者，该集合可能都不同。）我们确定了人口偏好及其（排名）选择行为的基于距离的排名模型。排名模型类似于曲棍球模型，但使用了称为反向主要索引（RMJ）的新距离函数。我们发现，尽管需要对所有排列进行汇总，但基于RMJ的排名分布骨料将其纳入（排名）选择概率，并具有简单的封闭形式表达式。我们开发有效的方法来估计模型参数并使用真实数据展示其概括功率，尤其是在显示集合有限的情况下。
We consider a preference learning setting where every participant chooses an ordered list of $k$ most preferred items among a displayed set of candidates. (The set can be different for every participant.) We identify a distance-based ranking model for the population's preferences and their (ranked) choice behavior. The ranking model resembles the Mallows model but uses a new distance function called Reverse Major Index (RMJ). We find that despite the need to sum over all permutations, the RMJ-based ranking distribution aggregates into (ranked) choice probabilities with simple closed-form expression. We develop effective methods to estimate the model parameters and showcase their generalization power using real data, especially when there is a limited variety of display sets.
