Supervised Dynamic Correlated Topic Model for Classifying Categorical Time Series

Abstract

In this paper, we describe the supervised dynamic correlated topic model (sDCTM) for classifying categorical time series. This model extends the correlated topic model used for analyzing textual documents to a supervised framework that features dynamic modeling of latent topics. sDCTM treats each time series as a document and each categorical value in the time series as a word in the document. We assume that the observed time series is generated by an underlying latent stochastic process. We develop a state-space framework to model the dynamic evolution of the latent process, i.e., the hidden thematic structure of the time series. Our model provides a Bayesian supervised learning (classification) framework using a variational Kalman filter EM algorithm. The E-step and M-step, respectively, approximate the posterior distribution of the latent variables and estimate the model parameters. The fitted model is then used for the classification of new time series and for information retrieval that is useful for practitioners. We assess our method using simulated data. As an illustration to real data, we apply our method to promoter sequence identification data to classify E. coli DNA sub-sequences by uncovering hidden patterns or motifs that can serve as markers for promoter presence.