Bayesian Inference for Vertex-Series-Parallel Partial Orders

Chuxuan Jiang, Geoff Keith Nicholls, Kate Lee

Keywords: Partial orders, bayesian inference, vertex-series-parallel partial orders, ranking models, linear extensions

TL;DR: This is the first work performing Bayesian inference on vertex-series-parallel partial orders (VSPs). We propose a prior over VSP's and extend an existing observation model for queue-like noisy rank 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.