A Closed Form Solution for Multiple-Input Spike Based Adaptive Filters

Neurons are point process systems, in the sense that the inputs and output which are spike trains can be treated as point processes. System identification of a point process system has been studied mostly with single input. However, multiple input is required in many applications such as liquid state machines or neural prosthetics. We propose a simple multiple-input spike based adaptive filter which is based on an integrate-and-fire neuron model. The optimal closed solution is derived, and the performance is analyzed with respect to noise in various parameters and measurement.