Todd Coleman (Electrical and Computer Engineering, University of Illinois)
Convex Optimization Techniques for Parametric and Nonparametric Statistical Analysis of Neural Data Using Point Processes
Abstract: Point process models have been shown to be useful in characterizing neural spiking activity as a function of extrinsic and intrinsic factors. First, we introduce a dynamical point process model for how complex sounds are represented by neural spiking in auditory nerve fibers. This point process model is the first to capture elements of spontaneous rate, refractory effects, frequency selectivity, phase locking at low frequencies, and short-term adaptation, within a compact parametric approach. Secondly, we consider nonparametric approaches for scenarios where the actual point process does not lie in the assumed parametric class. Such methods are attractive due to fewer assumptions, but most methods require excessively complex algorithms. We propose a computationally efficient method for nonparametric maximum likelihood estimation when the conditional intensity function, which characterizes the point process in its entirety, is assumed to satisfy a Lipschitz continuity condition. We show that by exploiting the structure of the likelihood function of a point process, the problem becomes efficiently solvable via Lagrangian duality and we compare our nonparametric estimation method to the most commonly used parametric approaches on goldfish retinal ganglion neural data and activity recorded in CA1 hippocampal neurons from an awake behaving rat. We show that our nonparametric method gives a superior absolute goodness-of-fit measure used for point processes than the most common parametric and semi-parametric approaches. joint work with - Andrea Trevino, graduate student, ECE, UIUC - Jont Allen, Assoc. Prof. ECE, UIUC - Sridevi Sarma, postdoctoral scholar, MIT |
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