Investigating Conditional Restricted Boltzmann Machines in Regime Detection

ArXiv ID: 2512.21823 “View on arXiv”

Authors: Siddhartha Srinivas Rentala

Abstract

This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted Boltzmann Machines (RBMs) by incorporating autoregressive conditioning and utilizing Persistent Contrastive Divergence (PCD) to incorporate complex temporal dependency structures. Comparing a discrete Bernoulli-Bernoulli architecture against a continuous Gaussian-Bernoulli variant across a multi-asset dataset spanning 2013-2025, we observe a dichotomy between generative fidelity and regime detection. While the Gaussian CRBM successfully preserves static asset correlations, it exhibits limitations in generating long-range volatility clustering. Thus, we analyze the free energy as a relative negative log-likelihood (surprisal) under a fixed, trained model. We demonstrate that the model’s free energy serves as a robust, regime stability metric. By decomposing the free energy into quadratic (magnitude) and structural (correlation) components, we show that the model can distinguish between pure magnitude shocks and market regimes. Our findings suggest that the CRBM offers a valuable, interpretable diagnostic tool for monitoring systemic risk, providing a supplemental metric to implied volatility metrics like the VIX.

Keywords: systemic risk, time series modeling, Restricted Boltzmann Machines, regime detection, financial time series

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper features dense statistical physics derivations, energy-based formulations, and complex probabilistic calculus, indicating high mathematical sophistication. It also includes concrete empirical analysis with multi-asset datasets (2013-2025), comparisons between Bernoulli and Gaussian architectures, and implementation-focused techniques like Persistent Contrastive Divergence, demonstrating solid empirical implementation.

  flowchart TD
    A["Research Goal:<br>Model financial time series<br>and detect systemic risk regimes<br>using Conditional RBMs"] --> B["Data & Models:<br>Multi-asset dataset<br>2013-2025<br>Discrete Bernoulli CRBM<br>Continuous Gaussian CRBM"]
    B --> C["Methodology:<br>Autoregressive Conditioning<br>Persistent Contrastive Divergence PCD"]
    C --> D{"Computation:<br>Analyze Free Energy<br>as relative negative log-likelihood"}
    D --> E["Decomposition:<br>Quadratic Component<br>Structural Component"]
    E --> F{"Findings/Outcomes"}
    F --> G["Generative Fidelity<br>Gaussian CRBM preserves static correlations<br>but struggles with volatility clustering"]
    F --> H["Systemic Risk Metric<br>Free energy serves as robust regime stability metric<br>distinguishing magnitude shocks vs market regimes"]