We investigate the Plackett-Luce (PL) model based listwise learning-to-rank (LTR) on data with partitioned preference, where a set of items are sliced into ordered and disjoint partitions, but the ranking of items within a partition is unknown. Given $N$ items with $M$ partitions, calculating the likelihood of data with partitioned preference under the PL model has a time complexity of $O(N+S!)$, where $S$ is the maximum size of the top $M-1$ partitions. This computational challenge restrains most existing PL-based listwise LTR methods to a special case of partitioned preference, top-$K$ ranking, where the exact order of the top $K$ items is known. In this paper, we exploit a random utility model formulation of the PL model, and propose an efficient numerical integration approach for calculating the likelihood and its gradients with a time complexity $O(N+S^3)$. We demonstrate that the proposed method outperforms well-known LTR baselines and remains scalable through both simulation experiments and applications to real-world eXtreme Multi-Label classification tasks.
翻译:我们调查了Plackett-Luce(PL)模型基于列表的学习到排名模型,该模型以偏好分隔区划的数据为基础,其中一组项目被切入定序和断开分割区,但分割区内的项目排名不详。如果使用美元分隔区划的项目为美元,则计算Plackett-Luce(PLackett-Luce)模型数据的可能性时复杂度为$O(N+S!)美元,其中美元是最高M-1美元分区的最大规模。这一计算性挑战将大多数现有的基于PLTR的列表方法限制在偏好区划区划区划的特例中,即最高-K$的排序,而最上-K$项目的确切顺序是已知的。在本文中,我们利用一个随机的PLP模型的实用模型,提出一个高效的数字集成法,用时间复杂度计算可能性及其梯度为$O(N+S%3美元)。我们证明,拟议的方法超越了众所周知的LTR基线,通过模拟实验和应用到现实世界的eXre-MLlabel任务,仍然可以调整。