System Identification from Neural Correlation

Abstract

The analysis of correlated neural activity can form the basis for constructing wiring diagrams of neural circuits (e.g., Stevens and Gerstein 1976; Toyama and Tanaka 1984). A wiring diagram is to be read as a scheme for the connectivity of the network, where additional graphical elements such as thickness or color of the wires may be used to indicate specific aspects of the connection, such as strength, sign, and latency (e.g., Gerstein et al. 1985 a). In general the “wiring” diagram approach tends to emphasize the gross aspects of the connectivity, not so much the detailed aspects such as precise time course of the interaction or the shape of the postsynaptic potentials. A more general use of input and output signals is to identify the system that is in between: this in general leads to a (non)linear model that describes the transformation from the input signal to output signal. From such a model the connection between two (or more) neurons can be derived. A necessary requirement for applying these techniques is that the system is time-invariant and has finite memory. These conditions may create some problems in biological systems. Thus the results and methods discussed in this chapter pertain only to nonlearning systems with time-invariant synaptic strengths.