Adaptive latent state modeling of brain network dynamics with real-time learning rate optimization

Objective. Dynamic latent state models are widely used to characterize the dynamics of brain network activity for various neural signal types. To date, dynamic latent state models have largely been developed for stationary brain network dynamics. However, brain network dynamics can be non-stationary for example due to learning, plasticity or recording instability. To enable modeling these non-stationarities, two problems need to be resolved. First, novel methods should be developed that can adaptively update the parameters of latent state models, which is difficult due to the state being latent. Second, new methods are needed to optimize the adaptation learning rate, which specifies how fast new neural observations update the model parameters and can significantly influence adaptation accuracy.Approach. We develop a Rate Optimized-adaptive Linear State-Space Modeling (RO-adaptive LSSM) algorithm that solves these two problems. First, to enable adaptation, we derive a computation- and memory-efficient adaptive LSSM fitting algorithm that updates the LSSM parameters recursively and in real time in the presence of the latent state. Second, we develop a real-time learning rate optimization algorithm. We use comprehensive simulations of a broad range of non-stationary brain network dynamics to validate both algorithms, which together constitute the RO-adaptive LSSM.Main results. We show that the adaptive LSSM fitting algorithm can accurately track the broad simulated non-stationary brain network dynamics. We also find that the learning rate significantly affects the LSSM fitting accuracy. Finally, we show that the real-time learning rate optimization algorithm can run in parallel with the adaptive LSSM fitting algorithm. Doing so, the combined RO-adaptive LSSM algorithm rapidly converges to the optimal learning rate and accurately tracks non-stationarities.Significance. These algorithms can be used to study time-varying neural dynamics underlying various brain functions and enhance future neurotechnologies such as brain-machine interfaces and closed-loop brain stimulation systems.