Continuous Time Dynamic Topic Models (1206.3298v2)

Abstract: In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a "topic" is a pattern of word use that we expect to evolve over the course of the collection. We derive an efficient variational approximate inference algorithm that takes advantage of the sparsity of observations in text, a property that lets us easily handle many time points. In contrast to the cDTM, the original discrete-time dynamic topic model (dDTM) requires that time be discretized. Moreover, the complexity of variational inference for the dDTM grows quickly as time granularity increases, a drawback which limits fine-grained discretization. We demonstrate the cDTM on two news corpora, reporting both predictive perplexity and the novel task of time stamp prediction.

• The paper introduces cDTM, which models continuous topic evolution using Brownian motion to overcome limitations of fixed time intervals.
• It employs an efficient variational inference algorithm that exploits data sparsity to reduce computational complexity and memory usage.
• Experimental results on news corpora demonstrate cDTM’s improved predictive accuracy and scalability across varied temporal resolutions.

Continuous Time Dynamic Topic Models

The paper presents the Continuous Time Dynamic Topic Model (cDTM), an advancement over traditional topic models like Latent Dirichlet Allocation (LDA) and the more specifically designed Discrete-Time Dynamic Topic Model (dDTM). The cDTM leverages Brownian motion to accommodate the temporal evolution of topics across a sequential document collection. This model is particularly useful for datasets where topics evolve continuously over time, such as news articles or scientific journals.

Core Contributions

The cDTM addresses two primary limitations of the dDTM. Firstly, dDTMs require discretization of time into fixed intervals, which can limit their application when fine granularity is necessary. As time granularity increases, computational complexity and memory requirements for dDTMs grow rapidly. In contrast, the cDTM models time as a continuum, which allows for arbitrary granularity in topic evolution without an associated increase in computational cost.

Secondly, the cDTM introduces an efficient variational inference algorithm that capitalizes on the inherent sparsity of text data. This approach avoids the need to represent probabilities at unobserved intervals between documents, thus reducing memory and computational demands significantly.

Methodology

The proposed method models the evolution of topics via Brownian motion, allowing for continuous change in topic parameters. The inference process involves a sparse variational method adapted from Kalman filtering techniques, which efficiently handles large vocabularies and multiple time points by focusing computations only on necessary parameters. This approach mitigates the computational inefficiencies encountered in densely parameterized models.

Experimental Insights

Experiments were conducted using two news corpora: a subset from the TREC AP corpus and the Election 08 data from Digg. The results illustrated the superior efficiency of the cDTM over dDTM when predicting time-stamped documents. The predictive perplexity and time stamp prediction accuracy demonstrated that cDTM performs effectively across different time granularities and dataset sparsities.

The cDTM's ability to handle varying temporal resolutions was especially beneficial when the data sparsity was high, reducing the need for memory resources compared to the dDTM. This efficiency is quantified by the notion of sparsity, which refers to the proportion of time intervals without document observations.

Implications and Future Work

The introduction of cDTM provides a robust framework for modeling time-series text data with continuous-time characteristics. This capability is vital for applications requiring fine temporal analysis without the overhead incurred by discrete models. Future research directions could explore extensions such as the Ornstein-Uhlenbeck process, providing bounded variance control in topic evolution.

The cDTM's design significantly impacts fields such as information retrieval and trend analysis, where understanding the temporal dynamics of topics offers critical insights. Further exploration of its application across varied domains, including real-time data streams and social media analysis, would enhance the model's practicality. Potential enhancements in adaptive inference strategies and scalability may also broaden cDTM's applicability to larger, more complex datasets.