Modeling Neural Connectivity in a Point-Process Analogue of Kalman Filter

A neural encoding model describes how single neuron tunes to external stimuli as well as its connectivity with other neurons. The connectivity illustrates the neuronal interaction within populations in response to the shared latent brain states. Understanding these interactions is crucial to computationally predict the neural activity, which elucidates the neural encoding mechanism A computational analysis on the neural connectivity also facilitates developing more point process decoding model to interpret movement state from neural spike observations for brain machine interfaces (BMI). Most of the previous point process models only consider single neural tuning property and assumes conditional independence among multiple neurons. The connectivity among neurons is not considered in such a Bayesian approach to derive the state. In this work, we propose a point-process analogue of Kalman Filter to model the neural connectivity in a closed-form Bayesian filter. Neural connectivity corrects the posterior of the state given the multi-dimension observation, and a Gaussian distribution is used to approximate the updated posterior distribution. We validate the proposed method on simulation data and compared with traditional point process filtering with conditional independent assumption. The result shows that our method models the neural connectivity information and the single neuronal tuning property at the same time and achieves a better performance of the state decoding. Clinical Relevance - This paper proposes a closed-form derivation of a point process filter based on Gaussian approximations. It can model both single neuronal tuning property and the neural connectivity, which is potential to understanding the neural connectivity computationally.