Nested Hierarchical Dirichlet Processes (1210.6738v4)

Abstract: We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, single-path formulation of the nCRP, allowing a document to more easily express thematic borrowings as a random effect. We derive a stochastic variational inference algorithm for the model, in addition to a greedy subtree selection method for each document, which allows for efficient inference using massive collections of text documents. We demonstrate our algorithm on 1.8 million documents from The New York Times and 3.3 million documents from Wikipedia.

• The paper's main contribution is the nHDP, which overcomes the nCRP's single-path constraint by allowing per-word thematic flexibility.
• The paper employs a stochastic variational inference algorithm that scales efficiently to millions of documents while reducing computational overhead.
• The paper demonstrates superior predictive log likelihood performance compared to traditional nCRP, stochastic LDA, and HDP models on diverse datasets.

An Expert Overview of "Nested Hierarchical Dirichlet Processes"

The paper "Nested Hierarchical Dirichlet Processes" introduces and explores the nested hierarchical Dirichlet process (nHDP), a significant advancement in hierarchical topic modeling. The nHDP addresses limitations in previous models such as the nested Chinese restaurant process (nCRP) by allowing documents to explore their thematic structure more flexibly through distinct paths in a shared topic tree. This is achieved by employing a per-document distribution over paths on the shared tree, a methodology that extends the stochastic framework of hierarchical Dirichlet processes (HDPs) to a nested contextual environment.

Advances Over the Nested Chinese Restaurant Process

The nHDP offers a robust solution to the rigidity in topic modeling imposed by the nCRP's single-path constraint, where every document is bound to selecting topics from one path in the hierarchical tree. Such a model is inefficient as it does not leverage the full thematic potential inherent in large, complex datasets, and results in either theme overgeneralization or the unnecessary proliferation of topics. The nHDP overcomes this by allowing each document to use different thematic paths per word, facilitating a more comprehensive combination of thematic elements.

Stochastic Variational Inference for Large Data

The authors derive a stochastic variational inference algorithm tailored to the nHDP. This algorithm supports efficient inference in large-scale text corpora by leveraging stochastic optimization techniques. It segregates the document-level variables from those shared among documents—reducing computational overhead and allowing scalability. The algorithm was demonstrated using 1.8 million documents from The New York Times and 2.7 million from Wikipedia, validating its effectiveness and practicality.

Numerical Performance and Comparative Analysis

Empirically, the proposed nHDP model outperformed both variational and Gibbs implementations of the nCRP. When applied to smaller datasets like The Journal of the ACM abstracts, Psychological Review abstracts, and Proceedings of the National Academy of Sciences abstracts, the nHDP showed superior predictive log likelihood performance, especially as data complexity and size increased. The stochastic model further exhibited better predictive log likelihood when benchmarked against stochastic LDA and HDP across large datasets, confirming its suitability for big data scenarios.

Implications and Future Directions

The implications of nHDP lie primarily in its potential to define more nuanced and structurally coherent thematic representations of text data. The nHDP provides a more precise mixture of topic representations at multiple specificities, which illustrates better conceptual overlapping among documents. This flexibility aids in pursuing applications where topic overlap and specificity are crucial, such as large-scale text analysis and natural language processing.

Future research could explore refining the stochastic variational inference further, especially concerning convergence speed and adaptability to varied corpus sizes. Another direction could involve integrating nHDP with other machine learning models to enhance its adaptability across different types of data beyond text, such as image or multisensory streams, where hierarchical decomposition is equally beneficial.

In summation, the work establishes a significant methodological stride in Bayesian nonparametric modeling. By outlining the nHDP, it presents a robust framework capable of handling thematic complexity and diversity in large-scale data through an elaborate, yet computationally feasible structure.