School of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan.
Neural Comput. 2010 Sep 1;22(9):2417-51. doi: 10.1162/NECO_a_00008.
Given a set of rating data for a set of items, determining preference levels of items is a matter of importance. Various probability models have been proposed to solve this task. One such model is the Plackett-Luce model, which parameterizes the preference level of each item by a real value. In this letter, the Plackett-Luce model is generalized to cope with grouped ranking observations such as movie or restaurant ratings. Since it is difficult to maximize the likelihood of the proposed model directly, a feasible approximation is derived, and the em algorithm is adopted to find the model parameter by maximizing the approximate likelihood which is easily evaluated. The proposed model is extended to a mixture model, and two applications are proposed. To show the effectiveness of the proposed model, numerical experiments with real-world data are carried out.
给定一组物品的评分数据，确定物品的偏好水平是很重要的。已经提出了各种概率模型来解决这个任务。其中一个模型是 Plackett-Luce 模型，它通过实数值来参数化每个项目的偏好水平。在这封信中，Plackett-Luce 模型被推广到处理分组排名观察，如电影或餐厅评分。由于直接最大化模型的似然性是困难的，因此导出了一个可行的近似值，并通过最大化易于评估的近似似然性来采用 EM 算法来找到模型参数。所提出的模型被扩展到混合模型，并提出了两个应用。为了展示所提出模型的有效性，使用真实数据进行了数值实验。
