title: Time resolution dependence of information measures for spiking neurons: scaling and universality.
abstract: The mutual information between stimulus and spike-train response is commonly used to monitor neural coding efficiency, but neuronal computation broadly conceived requires more refined and targeted information measures of input-output joint processes. A first step toward that larger goal is to develop information measures for individual output processes, including information generation (entropy rate), stored information (statistical complexity), predictable information (excess entropy), and active information accumulation (bound information rate). We calculate these for spike trains generated by a variety of noise-driven integrate-and-fire neurons as a function of time resolution and for alternating renewal processes. We show that their time-resolution dependence reveals coarse-grained structural properties of interspike interval statistics; e.g., τ-entropy rates that diverge less quickly than the firing rate indicated by interspike interval correlations. We also find evidence that the excess entropy and regularized statistical complexity of different types of integrate-and-fire neurons are universal in the continuous-time limit in the sense that they do not depend on mechanism details. This suggests a surprising simplicity in the spike trains generated by these model neurons. Interestingly, neurons with gamma-distributed ISIs and neurons whose spike trains are alternating renewal processes do not fall into the same universality class. These results lead to two conclusions. First, the dependence of information measures on time resolution reveals mechanistic details about spike train generation. Second, information measures can be used as model selection tools for analyzing spike train processes.
authors.affiliation: Department of Physics, University of California, Berkeley Berkeley, CA, USA.
authors.forename: Sarah E
authors.initials: SE
authors.lastname: Marzen
authors.affiliation: Department of Physics, University of California, Berkeley Berkeley, CA, USA ; Helen Wills Neuroscience Institute and Redwood Center for Theoretical Neuroscience, University of California, Berkeley Berkeley, CA, USA.
authors.forename: Michael R
authors.initials: MR
authors.lastname: DeWeese
authors.affiliation: Complexity Sciences Center and Department of Physics, University of California, Davis Davis, CA, USA.
authors.forename: James P
authors.initials: JP
authors.lastname: Crutchfield
keywords: 05.45.Tp 02.50.Ey 87.10.Vg 87.19.ll 87.19.lo 87.19.ls; alternating renewal process; entropy rate; excess entropy; integrate and fire neuron; leaky integrate and fire neuron; quadratic integrate and fire neuron; renewal process; statistical complexity