SNR estimation for nonlinear dynamical state-space models

Determine how to estimate the signal-to-noise ratio (SNR) when recovering latent states that evolve according to a nonlinear dynamical state-space model using neural population spike train observations, providing a concrete procedure or bound applicable to such nonlinear dynamics.

Background

The paper derives a practical upper bound on the signal-to-noise ratio (SNR) of inferred neural latent trajectories by leveraging Fisher information under a log-linear Poisson observation model. Using the Cramér–Rao bound, the analysis quantifies how tuning strength, firing rates, and the loading matrix contribute to SNR, and validates insights with simulations and a non-human primate dataset.

While the work focuses on Fisher information-based upper bounds and demonstrates improvements from temporal smoothing and increasing neuron counts, the authors note that their current analysis provides only an upper bound and depends on the assumed generative model. They explicitly identify as future work the problem of estimating SNR for latent processes governed by nonlinear dynamical state-space models, which goes beyond the log-linear Poisson framework analyzed here.