  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.
