CFTM: Continuous time fractional topic model

ArXiv ID: 2402.01734 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: fractional Brownian motion (fBm), dynamic topic modeling, long-range dependence, time series analysis, economic news, Information Services

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is mathematically dense, introducing advanced stochastic calculus via fractional Brownian motion and proving theoretical properties of parameter estimation, which drives a high complexity score. However, the empirical validation is limited to a single application (economic news articles) with no backtesting, performance metrics, or code/data links, resulting in low empirical rigor.
  flowchart TD
    A["Research Goal<br>Dynamic Topic Modeling with<br>Long-Term Dependencies"] --> B["Methodology<br>Proposed: cFTM using<br>Fractional Brownian Motion fBm"]
    B --> C["Data Input<br>Economic News Articles"]
    C --> D["Computational Process<br>Parameter Estimation<br>Complexity equivalent to LDA"]
    D --> E["Key Findings & Outcomes<br>1. Captures Long-Term Dependency/Roughness<br>2. Identifies Positive/Negative Correlations<br>3. Tracks Topics over Time"]