Convergence Properties of Some Spike-Triggered Analysis Techniques

Abstract

vVe analyze the convergence properties of three spike-triggered data analysis techniques. All of our results are obtained in the set(cid:173) ting of a (possibly multidimensional) linear-nonlinear (LN) cascade model for stimulus-driven neural activity. We start by giving exact rate of convergence results for the common spike-triggered average (STA) technique. Next, we analyze a spike-triggered covariance method, variants of which have been recently exploited successfully by Bialek, Simoncelli, and colleagues. These first two methods suf(cid:173) fer from extraneous conditions on their convergence; therefore, we introduce an estimator for the LN model parameters which is de(cid:173) signed to be consistent under general conditions. We provide an algorithm for the computation of this estimator and derive its rate of convergence. We close with a brief discussion of the efficiency of these estimators and an application to data recorded from the primary motor cortex of awake, behaving primates.