TY - GEN

T1 - A Hyper-surface Arrangement Model of Ranking Distributions

AU - Kaji, Shizuo

AU - Horiguchi, Akira

AU - Abe, Takuro

AU - Watanabe, Yohsuke

N1 - Funding Information:
This research was partially funded by ZOZO technologies inc.
Publisher Copyright:
© 2021 ACM.

PY - 2021/8/14

Y1 - 2021/8/14

N2 - A distribution on the permutations over a fixed finite set is called a ranking distribution. Modelling ranking distributions is one of the major topics in preference learning as such distributions appear as the ranking data produced by many judges. In this paper, we propose a geometric model for ranking distributions. Our idea is to use hyper-surface arrangements in a metric space as the representation space, where each component cut out by hyper-surfaces corresponds to a total ordering, and its volume is proportional to the probability. In this setting, the union of components corresponds to a partial ordering and its probability is also estimated by the volume. Similarly, the probability of a partial ordering conditioned by another partial ordering is estimated by the ratio of volumes. We provide a simple iterative algorithm to fit our model to a given dataset. We show our model can represent the distribution of a real-world dataset faithfully and can be used for prediction and visualisation purposes.

AB - A distribution on the permutations over a fixed finite set is called a ranking distribution. Modelling ranking distributions is one of the major topics in preference learning as such distributions appear as the ranking data produced by many judges. In this paper, we propose a geometric model for ranking distributions. Our idea is to use hyper-surface arrangements in a metric space as the representation space, where each component cut out by hyper-surfaces corresponds to a total ordering, and its volume is proportional to the probability. In this setting, the union of components corresponds to a partial ordering and its probability is also estimated by the volume. Similarly, the probability of a partial ordering conditioned by another partial ordering is estimated by the ratio of volumes. We provide a simple iterative algorithm to fit our model to a given dataset. We show our model can represent the distribution of a real-world dataset faithfully and can be used for prediction and visualisation purposes.

UR - http://www.scopus.com/inward/record.url?scp=85114906038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85114906038&partnerID=8YFLogxK

U2 - 10.1145/3447548.3467253

DO - 10.1145/3447548.3467253

M3 - Conference contribution

AN - SCOPUS:85114906038

T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

SP - 796

EP - 804

BT - KDD 2021 - Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

PB - Association for Computing Machinery

T2 - 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2021

Y2 - 14 August 2021 through 18 August 2021

ER -