Investigating Conditional Restricted Boltzmann Machines in Regime Detection

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.