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Vectorized Bayesian Inference for Latent Dirichlet-Tree Allocation

arXiv:2602.18795v1 Announce Type: new Abstract: 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 comput

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Zheng Wang, Nizar Bouguila · · 1 min read · 5 views
#cs.LG #stat.ML

arXiv:2602.18795v1 Announce Type: new Abstract: 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.

Executive Summary

This article introduces Latent Dirichlet-Tree Allocation (LDTA), a generalization of Latent Dirichlet Allocation (LDA) that replaces the Dirichlet prior with an arbitrary Dirichlet-Tree (DT) distribution. LDTA enables expressive, tree-structured priors over topic proportions while preserving LDA's generative structure. The authors develop universal mean-field variational inference and Expectation Propagation methods for LDTA, which are implemented in a fully vectorized and GPU-accelerated framework. This framework substantially expands the modeling capacity of LDA while maintaining scalability and computational efficiency. The authors demonstrate the effectiveness of LDTA in discovering latent thematic structure in discrete data.

Key Points

  • ▸ LDTA generalizes LDA by replacing the Dirichlet prior with an arbitrary Dirichlet-Tree (DT) distribution.
  • ▸ LDTA enables expressive, tree-structured priors over topic proportions.
  • ▸ Universal mean-field variational inference and Expectation Propagation methods are developed for LDTA.

Merits

Improved Modeling Capacity

LDTA substantially expands the modeling capacity of LDA by enabling tree-structured priors over topic proportions.

Scalability and Computational Efficiency

The fully vectorized and GPU-accelerated implementation of LDTA maintains scalability and computational efficiency.

Expressive Priors

LDTA enables expressive, tree-structured priors over topic proportions, which can capture rich correlations and hierarchical relationships.

Demerits

Complexity of Dirichlet-Tree Distribution

The Dirichlet-Tree distribution is complex and may require significant computational resources for inference.

Limited Interpretability

The tree-structured priors in LDTA may be difficult to interpret, which can limit the model's explanatory power.

Expert Commentary

The article presents a significant contribution to the field of topic modeling, introducing a new framework that enables expressive, tree-structured priors over topic proportions. The development of universal mean-field variational inference and Expectation Propagation methods for LDTA is a notable achievement, and the fully vectorized and GPU-accelerated implementation is a testament to the author's commitment to scalability and computational efficiency. However, the complexity of the Dirichlet-Tree distribution and the limited interpretability of the tree-structured priors are potential limitations of the model. Overall, the article is well-written and well-structured, and the results are compelling and well-supported by empirical evidence.

Recommendations

  • ✓ Future research should focus on developing more interpretable tree-structured priors for LDTA.
  • ✓ The authors should investigate the application of LDTA to other domains, such as image and audio processing.

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