Online Estimating Pairwise Neuronal Functional Connectivity in Brain-Machine Interface

Neurons respond to external stimuli and form functional networks through pairwise interactions. A neural encoding model can describe a single neuron's behavior, and brain-machine interfaces (BMIs) provide a platform to investigate how neurons adapt, functionally connect, and encode movement. Movement modulation and pairwise functional connectivity are modeled as high-dimensional tuning states, estimated from neural spike train observations. However, accurate estimation of this neural state vector can be challenging as pairwise neural interactions are highly dimensional, change in different temporal scales from movement, and could be non-stationary. We propose an Adam-based gradient descent method to online estimate high-dimensional pairwise neuronal functional connectivity and single neuronal tuning adaptation simultaneously. By minimizing negative log-likelihood based on point process observation, the proposed method adaptively adjusts the learning rate for each dimension of the neural state vectors by employing momentum and regularizer. We test the method on real recordings of two rats performing the brain control mode of a two-lever discrimination task. Our results show that our method outperforms existing methods, especially when the state is sparse. Our method is more stable and faster for an online scenario regardless of the parameter initializations. Our method provides a promising tool to track and build the time-variant functional neural connectivity, which dynamically forms the functional network and results in better brain control.