  Due to the inherent uncertainty of data, the problem of predicting partial
ranking from pairwise comparison data with ties has attracted increasing
interest in recent years. However, in real-world scenarios, different
individuals often hold distinct preferences. It might be misleading to merely
look at a global partial ranking while ignoring personal diversity. In this
paper, instead of learning a global ranking which is agreed with the consensus,
we pursue the tie-aware partial ranking from an individualized perspective.
Particularly, we formulate a unified framework which not only can be used for
individualized partial ranking prediction, but also be helpful for abnormal
user selection. This is realized by a variable splitting-based algorithm called
\ilbi. Specifically, our algorithm generates a sequence of estimations with a
regularization path, where both the hyperparameters and model parameters are
updated. At each step of the path, the parameters can be decomposed into three
orthogonal parts, namely, abnormal signals, personalized signals and random
noise. The abnormal signals can serve the purpose of abnormal user selection,
while the abnormal signals and personalized signals together are mainly
responsible for individual partial ranking prediction. Extensive experiments on
simulated and real-world datasets demonstrate that our new approach
significantly outperforms state-of-the-art alternatives. The code is now
availiable at https://github.com/qianqianxu010/NeurIPS2019-iSplitLBI.
