A Point Process Framework for Relating Neural Spiking Activity to Spiking History, Neural Ensemble, and Extrinsic Covariate Effects

Abstract

Donoghue, and Emery N. Brown. A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. J Neurophysiol 93: 1074 -1089, 2005. First published September 8, 2004 doi:10.1152/jn.00697.2004. Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron's spiking probability to three typical covariates: the neuron's own spiking history, concurrent ensemble activity, and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron's spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and non-GLM likelihood functions using simulated data and multivariate single-unit activity data simultaneously recorded from the motor cortex of a monkey performing a visuomotor pursuit-tracking task. The point process framework provides a flexible, computationally efficient approach for maximum likelihood estimation, goodness-of-fit assessment, residual analysis, model selection, and neural decoding. The framework thus allows for the formulation and analysis of point process models of neural spiking activity that readily capture the simultaneous effects of multiple covariates and enables the assessment of their relative importance.

Statistical Models of Spike Trains

“…Reprinted with permission of the Journal of Neursocience. the standard model selection approaches (Burnham and Anderson, 2002;Truccolo et al, 2005). From the point of view of analyzing a particular set of spike-train data, the decision whether to rely on IF models must consider interpretation, computational effort, and ability to account for apparent features of the data.…”

“…The point-process likelihood function is then given by the simple and explicit pdf (Snyder and Miller, 1991;Brown et al, 2003;Paninski, 2004;Truccolo et al, 2005) …”

“…in equation (9) is taken to be the exponential function, then the multiplicative and additive IMI models coincide. The additive formulation has become popular recently (Brillinger, 1988;Chornoboy et al, 1988;Brillinger, 1992;Paninski, 2004;Truccolo et al, 2005;Paninski et al, 2007b), largely because stimulus terms (e.g., if we set y(t) = a i x i (t), given the stimulus x(t)) and spike history terms are treated in a unified, linear manner within the nonlinear function f (.) (for this reason, the additive model is often described as a "generalized linear model").…”

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

“…The main challenge is that point process spike train data is not suitable for modelling by linear VAR models. A theoretically principled approach is to replace the VAR modelling step with fitting of full and reduced point process models, within a framework of maximum likelihood estimation (Okatan et al, 2005;Truccolo et al, 2005;Kim et al, 2011;Gerhard et al, 2013). The MVGC toolbox does not support this in its current version.…”

The use of computational modeling to link sensory processing with behavior in Drosophila

“…Alternatives to the STA method have been developed that permit identifying the filter without the strong requirement of uncorrelatedness of input statistics (Truccolo et al 2005;Pillow et al 2008;Sharpee 2013;Williamson et al 2015;Aljadeff et al 2016). These methods find the filter by directly minimizing the mismatch between the prediction of the model and the experimentally measured response using numerical optimization techniques in which the filter shape is modified gradually over many iterations to improve model fit.…”