Partial Order Ranking with SMC and Plackett–Luce Models

Ranking estimation under partial observations and time-varying order structure.

Problem

How can ranking models cope when only partial orders are observed and the underlying order itself evolves over time?

Method

Extended the Plackett–Luce model into a multi-weight formulation, then embedded it inside a hidden Markov structure observed through random linear extensions, with Sequential Monte Carlo and MCMC resampling for estimation.

Demonstrates

Going from mathematical structure (partial orders, stochastic processes) to a computational ranking method suited for high-dimensional and dynamic systems.

This dissertation studies ranking under partial observations, where the full order cannot be seen directly and may shift over time.

The classical Plackett–Luce model is generalized so each element carries multiple weights, allowing it to express relative position more flexibly than a single-weight model. The order itself is treated as a latent stochastic process, observed through random linear extensions of partial suborders at sequential sampling times.

Estimation uses Sequential Monte Carlo with MCMC resampling. Compared to a baseline MCMC approach, SMC with metropolis-coupled mixing improves stability on high-dimensional and dynamic problems, and offers a tractable path for online ranking estimation.