Learning-to-Rank with Partitioned Preference: Fast Estimation for the Plackett-Luce Model
This work addresses a computational bottleneck in learning-to-rank for applications like e-commerce and recommendation systems, enabling more efficient handling of partitioned preference data, though it is incremental as it builds on existing Plackett-Luce models.
The paper tackles the computational challenge of estimating the Plackett-Luce model for learning-to-rank with partitioned preference data, where item rankings within partitions are unknown, by proposing an efficient numerical integration method that reduces time complexity from O(N+S!) to O(N+S^3). The method outperforms existing baselines in simulations and real-world eXtreme Multi-Label classification tasks, demonstrating scalability and improved performance.
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.