In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in topic and word distribution over time, revealing long-term dependency or roughness. Our theoretical analysis shows that the cFTM can capture these long-term dependency or roughness in both topic and word distributions, mirroring the main characteristics of fBm. Moreover, we prove that the parameter estimation process for the cFTM is on par with that of LDA, traditional topic models. To demonstrate the cFTM's property, we conduct empirical study using economic news articles. The results from these tests support the model's ability to identify and track long-term dependency or roughness in topics over time.

Chien Lu received a runner up award for best student paper at ACML 2021. In this interview, he tells us about the implications of this research, the methodology, and plans for future work. Our paper is entitled "Cross-structural factor-topic model: document analysis with sophisticated covariates." This paper proposes a novel topic model to analyze text documents with sophisticated covariates. Text data are usually accompanied by various numerical covariates in many real-world situations.