What do spikes stand for?
Many of us would like to have better methods for characterizing the response of neurons to complex, naturalistic stimuli. Over the years, many different things have been tried: linear and nonlinear response measures according to Wiener and Volterra, the reverse correlation method which might (or might not) be the same thing, response conditional ensembles, spike triggered covariance matrices and spectrograms (corresponding to the spectrotemporal receptive fields), and so on. The goal of this talk is partly pedagogical: to show how these ideas relate to each other and to the even simpler idea of plotting firing rate vs. relevant stimulus parameters. All of these methods (should) provide a way of simplifying the problem, and I will suggest that the most interesting simplification is the idea of dimension reduction, which is hidden in most of these methods. I will try to make this idea explicit, and show how it can be used to characterize (at least in principle) profoundly nonlinear systems. I will give a short summary of data analyzed with this idea in mind, showing some interesting things that I don't think could have been found any other way. I will emphasize that this approach to characterizing neural responses can be automated only halfway ... one still needs some inspiration in order to complete the task.