A kernel approach to learning a neuron model from spike train data

A spiking neuron is a principal component of the brain and the nervous system. Understanding the characteristics of a single neuron as well as the interactions of a population of neurons is essential to neuroscience. At the micro-level, neurons are very complex devices that control the flow of ions in and out of the membrane. However an abstracted view of the neuron sees it as a mechanism which receives electrical signals from other neurons as input and produces and transmits electrical signals to other neurons. Much work has been done to model the neuron at varying levels of complexity in order to explain its dynamics. Competitions exist which compare the accuracy of submitted neurons models.;Here we propose a methodology which learns an equivalent mathematical mapping from input spike trains to the output spike train by only considering the timing of all afferent(incoming) and efferent(outgoing) spikes within a bounded finite past. This is done by instantiating a classiffication problem which uses kernels to dichotomize input spike trains which cause the neuron to generate a spike from those that do not cause the neuron to generate a spike. The kernel used is one that has been generated from a dictionary of functions which are similar to those used in existing neuron models. By using an intuitive dictionary, we produce a kernel which is tailored to the problem of learning spiking neuron models.;By the representer theorem we know that only a finite number of training data points will be needed to produce the classification solution. By considering the number of data points used to produce the solution, we are able to assess the complexity of the modeled neuron. Those neurons which need more spike time inputs to reproduce their behavior could be considered more complex than those which need fewer spike time inputs for the given kernel.