用树形先验改进传统主题模型，让主题间关系更丰富。
Vectorized Bayesian Inference for Latent Dirichlet-Tree Allocation
- 用狄利克雷树替代原有先验，建模主题间的层次关联
- 提出可向量化计算的变分推断方法，支持高效推理
- 适用于需捕捉主题层级结构的文本分析任务
潜在狄利克雷分配（LDA）是发现离散数据中隐含主题结构的基础模型，但其狄利克雷先验无法表达主题间常见的复杂相关性和层次关系。本文提出潜在狄利克雷树分配（LDTA），将LDA的狄利克雷先验推广为任意狄利克雷树（DT）分布，保持生成结构的同时，支持对主题比例的树状结构先验建模。为实现推断，我们开发了通用的均值场变分推断与期望传播方法，提供对所有狄利克雷树的可计算更新。通过理论分析揭示两种方法的向量化特性，并实现完全向量化、基于GPU加速的实现。该框架显著扩展了LDA的建模能力，同时保持可扩展性与计算效率。
原文摘要 · Abstract (English)
Latent Dirichlet Allocation (LDA) is a foundational model for discovering latent thematic structure in discrete data, but its Dirichlet prior cannot represent the rich correlations and hierarchical relationships often present among topics. We introduce the framework of Latent Dirichlet-Tree Allocation (LDTA), a generalization of LDA that replaces the Dirichlet prior with an arbitrary Dirichlet-Tree (DT) distribution. LDTA preserves LDA's generative structure but enables expressive, tree-structured priors over topic proportions. To perform inference, we develop universal mean-field variational inference and Expectation Propagation, providing tractable updates for all DT. We reveal the vectorized nature of the two inference methods through theoretical development, and perform fully vectorized, GPU-accelerated implementations. The resulting framework substantially expands the modeling capacity of LDA while maintaining scalability and computational efficiency.
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