Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering

Abstract

Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt their representations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new filters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the receptive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.

Brain correlates of autonomic modulation: Combining heart rate variability with fMRI

“…A novel adaptive recursive algorithm was applied to the R-R series to compute instantaneous estimates of heart rate and heart rate variability from electrocardiogram recordings of R-wave events. This approach is based on the point process methods for neural spike train data analysis Barbieri et al 2004;Eden et al 2004) already used to develop both local likelihood (Barbieri et al 2005) and adaptive (Barbieri et al 2006) heart rate estimation algorithms. The stochastic structure in the R-R intervals is modeled as an inverse Gaussian renewal process.…”

A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

“…These data can be analyzed with decoding algorithms, i.e. state-space estimation procedures, by extending the current algorithm to construct mixed filter algorithms for continuous observations and point processes (continuous time binary processes) in either discrete or continuous time (Eden et al 2004;Snyder and Miller 1991). Second, the mixed filter algorithm may make it possible to use simultaneously recorded ensemble neural spiking activity and local field potentials to control neural prosthetic devices and brain machine interfaces (Musallam et al 2004;Serruya et al 2002;Taylor et al 2002;Wessberg et al 2005).…”

“…As the dimension of the system increases, numerical computation becomes less feasible. A standard approach, and the one we derive in the appendix and apply here, is to compute Gaussian approximations to (5) and (6) (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003). This approach which is also termed maximum a posteriori estimation (Mendel 1995), amounts to finding the maximum and curvature of (5) as a function of the state x k .…”

“…To approximate a unimodal probability density f(x) with a Gaussian probability density we compute its mode μ̂ as the solution to the equation (Tanner 1996) (A.1) and its variance σ̂2 as (A.2) We derive the mixed filter algorithm by computing a Gaussian approximation to the posterior density p(x k |Z k , N k ) in (5), (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003). At trial k, we assume that the one-step prediction probability density in (6) is the Gaussian probability (A.3) The probability density for the continuous performance measures is (A.4) and the probability mass function for the binary performance measures is given in (3).…”

“…Applications of this paradigm range from control systems (Kitagawa and Gersch 1996;Mendel 1995), speech recognition (Becchetti and Ricotti 1999), studies of protein structure (White et al 1994), analysis of genetic networks (Harbison et al 2004), studies of neural representations of biological signals (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003) and analyses of learning (Wirth et al 2003;Smith et al 2004). A state-space model consists of two equations: a state equation and an observation equation.…”