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.
翻译:我们考虑一个优先学习环境,让每个参与者在一组显示的候选人中选择一份定购的、最偏好的项目的K美元清单。 (这套组合对每个参与者来说可能有所不同。 )我们为人口的偏好及其(排列顺序的)选择行为确定一个基于远程的排名模式。 排名模式类似于Mallows模式,但使用新的距离函数,称为逆向主要指数(RMJ ) 。 我们发现,尽管需要对所有变化进行总和,但基于RMJ的排名分配总和以(排序的)选择概率为简单封闭式表达方式。我们开发了有效的方法,用真实数据来估计模型参数并展示其一般化能力,特别是当显示器种类有限时。