A Generalized Model for Multidimensional Intransitivity
Jiuding Duan, Jiyi Li, Yukino Baba, Hisashi Kashima
TL;DR
The paper tackles the challenge of modeling intransitive pairwise preferences by introducing a generalized multidimensional embedding that jointly learns a player representation and a dataset-specific metric, formalized as $M^{G}(a,b)=\mathbf{a}^{T}\Sigma\mathbf{b}+\mathbf{a}^{T}\Gamma\mathbf{a}-\mathbf{b}^{T}\Gamma\mathbf{b}$ with symmetry guarantees. It demonstrates that the Blade-Chest family is a special case of this framework and provides an efficient training scheme with reparameterization to enforce symmetry, coupled with regularization terms to control scale. A thorough empirical study across sushi, Jester, MovieLens, election, SF4, and Dota datasets reveals pervasive intransitivity and shows the proposed method often achieves superior predictive accuracy compared to Naive, BT, and BC baselines. The work also offers the first quantitative examination of intransitivity in widely used benchmarks, highlighting the practical implications for recommendation, social choice, and online game analytics.
Abstract
Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain and has been long discussed in social choice theory in the context of the dominance relationship. However, such multifaceted intransitivity between players and the corresponding player representations in high dimensions is difficult to capture. In this paper, we propose a probabilistic model that jointly learns each player's d-dimensional representation (d>1) and a dataset-specific metric space that systematically captures the distance metric in Rd over the embedding space. Interestingly, by imposing additional constraints in the metric space, our proposed model degenerates to former models used in intransitive representation learning. Moreover, we present an extensive quantitative investigation of the vast existence of intransitive relationships between objects in various real-world benchmark datasets. To our knowledge, this investigation is the first of this type. The predictive performance of our proposed method on different real-world datasets, including social choice, election, and online game datasets, shows that our proposed method outperforms several competing methods in terms of prediction accuracy.