Decoding spike train ensembles: tracking a moving stimulus

We consider the issue of how to read out the information from nonstationary spike train ensembles. Based on the theory of censored data in statistics, we propose a 'censored' maximum-likelihood estimator (CMLE) for decoding the input in an unbiased way when the spike activity is observed over time windows of finite length. Compared with a rate-based, moment estimator, the CMLE is proved consistently more efficient, particularly with nonstationary inputs. Using our approach, we show that a dynamical input to a group of neurons can be inferred accurately and with high temporal resolution (50 ms) using as few as about one spike per neuron within each decoding window. By applying our theoretical results to a population coding setting, we then demonstrate that a spiking neural network can encode spatial information in such a way to allow fast and precise tracking of a moving target.