Distinguishing Feature Model for Ranking From Pairwise Comparisons

Elisha Parhi, Arun Rajkumar

Abstract: We consider the problem of ranking a set of items from pairwise comparisons among them when the underlying preferences are intransitive in nature. Intransitivity is a common occurrence in real world data sets and we introduce a flexible and natural parametric model for pairwise comparisons that we call the \emph{Distinguishing Feature Model} (DF) to capture this. Under this model, the items have an unknown but fixed embedding and the pairwise comparison between a pair of items depends probabilisitically on the feature in the embedding that can best distinguish the items. We study several theoretical properties including how it generalizes the popular transitive Bradley-Terry-Luce model. With just an embedding dimension $d = 3$, we show that the proposed model can capture arbitrarily long cyclic dependencies. Furthermore, we explicitly show the type of preference relations that cannot be modelled under the DF model for $d=3$. On the algorithmic side, we propose a Siamese type neural network based algorithm which can learn to predict well under the DF model while at the same time being interpretable in the sense that the embeddings learnt can be extracted directly from the learnt model. Our experimental results show that the model outperforms standard baselines in both synthetic and real world ranking datasets.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Deep Learning and representational learning