Predicting the nonlinear dynamics of biological neurons using support vector machines with different kernels

Based on biological data we examine the ability of support vector machines (SVMs) with Gaussian, polynomial and tanh-kernels to learn and predict the nonlinear dynamics of single biological neurons. We show that SVMs for regression learn the dynamics of the pyloric dilator neuron of the Australian crayfish, and we determine the optimal SVMs parameters with regard to the test error. Compared to conventional RBF networks and MLPs, SVMs with Gaussian kernels learned faster and performed a better iterated one-step-ahead prediction with regard to training and test error. From a biological point of view SVMs are especially better in predicting the most important part of the dynamics, where the membrane potential is driven by superimposed synaptic inputs to the threshold for the oscillatory peak.