The GLM has been fit to multi-electrode extracellular recordings from macaque retina, and accurately predicts how stimuli are transformed into the spike trains of a group of neurons. Given the observed spike trains of a population of cells, the estimated stimulus may be obtained by maximizing the posterior probability defined by the GLM model. This maximum is unique, and the computation is efficient, scaling linearly with the stimulus duration. We verify the accuracy of these estimates by developing stochastic sampling algorithms (Markov chain Monte Carlo), whose computation also scales linearly with stimulus duration. We show that direct model-based computation of the mutual information is tractable even in the case of large observed neural populations, where methods based on binning the spike train fail.

We use this optimal estimator as the basis for a new metric that expresses the similarity of two spike trains based on the Euclidean distance between their associated reconstructed stimuli. We use this metric to examine the relative importance of individual spikes and local spike patterns in ensembles of spike trains. In particular, the relative cost of spike shifts vs. removals and additions is dictated by the model in a principled way. The form of this metric also reveals the importance of correlated shifts in the timing of spikes, and can therefore serve as an efficient and valuable tool for exploring the nature of neural coding.