# Bayesian Inference for Vertex-Series-Parallel Partial Orders

arXiv: https://arxiv.org/abs/2306.15827 · HTML: https://mlsanity.com/paper/2306.15827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2023.

## Built on by (most cited first, 1 of 1)

- [A Differentiable Bayesian Relaxation for Latent Partial-Order Inference](https://mlsanity.com/paper/2605.06976/) (2026)

## Abstract (arXiv)

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.