Bayesian Inference for Vertex-Series-Parallel Partial Orders

TL;DR

This paper introduces a Bayesian framework for analyzing vertex-series-parallel partial orders, enabling efficient inference in social hierarchy models and demonstrating superior data fit compared to existing models.

Contribution

It develops a closed-form prior for VSPs and extends an observation model for noisy rank-order data, facilitating Bayesian inference on social hierarchy data.

Findings

Model outperforms Plackett-Luce and Mallows models in data fit

Provides a closed-form prior for VSPs with a controllable depth parameter

Demonstrates effective inference on real-world social hierarchy data

Abstract

Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few tens of elements is prohibitive. Vertex-series-parallel partial orders (VSPs) are a subclass of partial orders which admit rapid counting and represent the sorts of relations we expect to see in a social hierarchy. However, no Bayesian analysis of VSPs has been given to date. We construct a marginally consistent family of priors over VSPs with a parameter controlling the prior distribution over VSP depth. The prior for VSPs is given in closed form. We extend an existing observation model for queue-like rank-order data to represent noise in our data and carry out Bayesian inference on "Royal Acta" data and Formula 1 race data. Model comparison shows our model is a better fit to the data than Plackett-Luce mixtures, Mallows mixtures, and "bucket order" models and competitive with more complex models fitting general partial orders.