Stochastic Variational Inference for Dynamic Correlated Topic Models

Correlated topic models (CTM) are useful tools for statistical analysis of documents. They explicitly capture the correlation between topics associated with each document. We propose an extension to CTM that models the evolution of both topic correlation and word co-occurrence over time. This allows us to identify the changes of topic correlations over time, e.g., in the machine learning literature, the correlation between the topics "stochastic gradient descent" and "variational inference" increased in the last few years due to advances in stochastic variational inference methods. Our temporal dynamic priors are based on Gaussian processes (GPs), allowing us to capture diverse temporal behaviours such as smooth, with long-term memory, temporally concentrated, and periodic. The evolution of topic correlations is modeled through generalised Wishart processes (GWPs). We develop a stochastic variational inference method, which enables us to handle large sets of continuous temporal data. Our experiments applied to real world data demonstrate that our model can be used to effectively discover temporal patterns of topic distributions, words associated to topics and topic relationships.