Minimum-order Wiener modelling of spike-output systems

Systems that generate spike outputs in response to continuous inputs abound in neurophysiology. The study of their dynamics with the use of systems analysis methods has been complicated by the difference in modality of the input and output signals. When the problem is placed in the framework of Wiener's theory in discrete time, an infinite functional series is required for the formal representation of the input-output relation. This has given rise to the belief that a large number of Wiener functionals is needed in practice before a model of reasonable accuracy can be obtained. In this paper, we introduce the concept of minimum-order Wiener models for spike-output systems, and we show that a low-order Wiener model is adequate in many cases for predicting fully the timing of the output spikes.