Bayesian inference on partial orders from random rank-order data

Thesis

Ranking problems are prevalent across various fields, yet most existing models focus on reconstructing total orders rather than partial orders. Models parameterised by partial orders make weaker assumptions about the unknown underlying order relations. This thesis proposes a new class of generic ranking models parameterised by partial orders. We study their properties and develop efficient computational methods for Bayesian inference.

We develop partial order ranking models on both homogeneous and heterogeneous rank-order data. The proposed models are in general marginally consistent and provide control over partial order depth, properties that are not inherently provided by traditional models. We extend our basic model in several ways. Ties between elements of the partial order are modeled using non-parametric clustering and the “dimension” of the partial order is estimated using a separate non-parametric approach. Although partial orders offer great generality, inference can be formidable on large datasets. We work with vertex-series-parallel partial orders (VSPs), a scalable class that can be parameterized using binary decomposition trees. We develop statistical models for random VSPs and propose scalable inference schemes. For heterogeneous setting where rank-orders are provided by various assessors, we introduce a hierarchical partial order model (HPO) with a tree-like parameter-dependence structure. This model specifies a global partial order that governs “leaf” partial orders representing individual assessor preferences, complemented by a VSP approximation approach.

We also address observation errors inherent in rank-order data by investigating various noise models which sit on top of partial order models, including the Mallows model and the Plackett-Luce model. We extend the “queue-jumping” model to incorporate bi-directional queue-jumping behavior, aligning more closely with real-world scenarios.

While our partial order ranking models are primarily applied to social hierarchy studies, their utility extends to a wide range of ranking problems. We demonstrate their application to analysis of multi-player competition outcomes, user preference data, and more. Comparative analysis shows that our models are advantageous due to their flexibility in capturing diverse preference behaviors.

Authors: Jiang, C

• DOI: 10.5287/ora-nr4exknn8
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: partial orders; directed acyclic graph; ranking; Bayesian
• Subjects: Statistcs