Learning Heterogeneous Ordinal Graphical Models via Bayesian Nonparametric Clustering

TL;DR

This paper introduces a Bayesian nonparametric clustering method for ordinal graphical models, enabling flexible subgroup discovery and structure learning in complex systems like sports analytics.

Contribution

It proposes a novel MFM-based framework for modeling heterogeneous ordinal data with automatic cluster number estimation and efficient inference algorithms.

Findings

Successfully models heterogeneity in ordinal data

Automatically determines the number of subgroups

Provides robust structure estimation within each subgroup

Abstract

Graphical models are powerful tools for capturing conditional dependence structures in complex systems but remain underexplored in analyzing ordinal data, especially in sports analytics. Ordinal variables, such as team rankings, player performance ratings, and survey responses, are pervasive in sports data but present unique challenges, particularly when accounting for heterogeneous subgroups, such as teams with varying styles or players with distinct roles. Existing methods, including probit graphical models, struggle with modeling heterogeneity and selecting the number of subgroups effectively. We propose a novel nonparametric Bayesian framework using the Mixture of Finite Mixtures (MFM) approach to address these challenges. Our method allows for flexible subgroup discovery and models each subgroup with a probit graphical model, simultaneously estimating the number of clusters and their configurations. We develop an efficient Gibbs sampling algorithm for inference, enabling robust estimation of cluster-specific structures and parameters. This framework is particularly suited to sports analytics, uncovering latent patterns in player performance metrics. Our work bridges critical gaps in modeling ordinal data and provides a foundation for advanced decision-making in sports performance and strategy.