Imani Beckett's new framework uncovers hidden state-dependent volatility
Modeling latent systems where randomness depends on the underlying state
Most latent state-space models assume constant process variance, ignoring that variability in biological, behavioral, and physiological systems often depends on the underlying state. Imani Beckett's new framework tackles this by introducing a state-coupled stochastic volatility component, where latent process variance is a function of displacement from equilibrium. The method uses a particle expectation-maximization procedure that combines bootstrap particle filtering with backward trajectory smoothing to estimate both latent states and a coupling parameter $\gamma$ that quantifies the strength of this dependency.
In a large-scale simulation benchmark across varying coupling strengths, observation noise levels, trajectory lengths, and persistence regimes, the framework consistently reduced recovery bias compared to an observed-state heteroskedastic proxy. Improvements were largest under strong coupling and high observation noise, while detection remained competitive across conditions. This work provides a practical foundation for studying state-dependent variability, showing that structured stochasticity conveys information beyond mean-state trajectories—relevant for neuroscience, finance, and any field with partially observed nonlinear dynamics.
- Introduces coupling parameter γ that quantifies how latent state position affects process variance
- Uses particle expectation-maximization with backward smoothing to estimate state-dependent volatility under partial observation
- Simulation benchmark shows up to significant bias reduction under strong coupling and high observation noise
Why It Matters
Enables ML models to extract meaningful signals from variability itself, not just mean trajectories.