System Identification of Adapting Neurons

This report investigates how neurons with complex dynamics, specifically adaptation, can be incorporated into the Neural Engineering Framework. The focus of the report is fitting a linear-nonlinear system model to an adapting neuron model using system identification techniques. By characterizing the neuron dynamics in this way, we hope to gain a better understanding of what sort of temporal basis the neurons in a population provide, which will determine what kinds of dynamics can be decoded from the neural population. The report presents four system identification techniques: a correlation-based method, a least-squares method, an iterative least-squares technique based of Paulin’s algorithm, and a general iterative least squares method based of gradient descent optimization. These four methods are all used to fit linear-nonlinear models to the adapting neuron model. We find that the Paulin least-squares method performs the best in this situation, and linear-nonlinear models fit in this manner are able to capture the relevant adaptation dynamics of the neuron model. Other questions related to the system identification, such as the type of input to use and the amount of regularization required for the least-squares methods, are also answered empirically. The report concludes by performing system identification on 20 neurons with a range of adaptation parameters, and examining what type of temporal basis these neurons provide.