Control Analysis and Design for Statistical Models of Spiking Networks

A popular approach to characterizing activity in neuronal networks is the use of statistical models that describe neurons in terms of their firing rates (i.e., the number of spikes produced per unit time). The output realization of a statistical model is, in essence, an $n-$ dimensional binary time series, or pattern. While such models are commonly fit to data, they can also be postulated de novo, as a theoretical description of a given spiking network. More generally, they can model any network producing binary events as a function of time. In this paper, we rigorously develop a set of analyses that may be used to assay the controllability of a particular statistical spiking model, the point-process generalized linear model. Our analysis quantifies the ease or difficulty of inducing desired spiking patterns via an extrinsic input signal, thus providing a framework for basic network analysis, as well as for emerging applications such as neurostimulation design.