通过贝叶斯非参数聚类学习异质序图模型
Learning Heterogeneous Ordinal Graphical Models via Bayesian Nonparametric Clustering
AI总结：
本文提出一种非参数贝叶斯框架，通过混合有限混合方法，解决有序数据建模中的异质性问题，实现灵活的子群体发现和参数估计，适用于体育分析中的潜在模式识别。
摘要：
图模型是捕捉复杂系统中条件依赖结构的强大工具，但在分析有序数据方面仍处于探索阶段，尤其是在体育分析中。有序变量，如球队排名、球员表现评分和调查回应，广泛存在于体育数据中，但存在独特挑战，特别是在考虑异质子群体时，如风格各异的球队或角色不同的球员。现有方法，包括概率图模型，难以有效建模异质性并选择子群体数量。我们提出了一种新的非参数贝叶斯框架，采用有限混合混合（MFM）方法来解决这些问题。我们的方法允许灵活发现子群体，并用概率图模型对每个子群体进行建模，同时估计集群数量及其配置。我们开发了高效的吉布斯采样算法用于推断，使能够稳健地估计集群特定的结构和参数。该框架特别适用于体育分析，揭示球员表现指标中的潜在模式。我们的工作填补了对有序数据建模的关键空白，并为体育表现和策略的高级决策提供了基础。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
