A Semiparametric Bayesian Model for Detecting Synchrony Among Multiple Neurons

Abstract

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1’s (spike) and 0’s (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a Gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows: the nonparametric component (i.e., the Gaussian process model) provides a flexible framework for modeling the underlying firing rates; the parametric component (i.e., the copula model) allows us to make inference regarding both contemporaneous and lagged relationships among neurons; using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of dependence structure among variables; our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas.

Copula Regression Analysis of Simultaneously Recorded Frontal Eye Field and Inferotemporal Spiking Activity during Object-Based Working Memory

“…The neural dependencies have been characterized by copula models based on the distribution of either the spike counts (Berkes et al, 2009) or the interspike intervals (Sacerdote et al, 2012;Hu et al, 2015). A recent study has shown that the synchronous spiking among multiple neurons can be detected using the copula model, whereby the parameters in the model can be estimated within a semiparametric Bayesian framework (Shahbaba et al, 2014). Recently, a copula-based Granger causality measure has been developed for a continuous time series of field potentials to capture nonlinear and high-order moment causality in the neural data (Hu and Liang, 2014).…”

A Dynamic Bayesian Model for Characterizing Cross-Neuronal Interactions During Decision-Making

“…More specifically, we demonstrate that our model can identify time-varying dependencies while methods based on static models such as the methods of Kass et al (2011) and Shahbaba et al (2014) provide an incomplete picture of neuronal activity and, moreover, could give misleading results. To compare our proposed approach to those in Kass et al (2011) and Shahbaba et al (2014), we first generate spike trains for a pair of neurons for which ζ t follows the pattern shown in the left panel of Figure 4. Due to the assumption that the correlation structure is stationary, the method of Kass et al (2011) reports a p-value of 0.555 for the test of H 0 : ζ = 1 (independence) vs. H a : ζ ≠ 1.…”

“…As mentioned in the introduction, our approach is related to a number of existing methods such as the GLM-based method of Kass et al (2011) and Kelly and Kass (2012), the semi-parametric model of Shahbaba et al (2014), and copula-based models of Wilson and Ghahramani (2012) and Swihart et al (2010). Our method is also related to the model proposed by Cunningham et al (2007), who assume that the underlying non-negative firing rate for spike train is a draw from a Gaussian process.…”

“…However, to capture complex behavior of neural networks, many new statistical methods have been recently proposed for analyzing several simultaneously recoded neurons in order to extract information contained in their temporal interactions under different experimental conditions. For more discussion on analysis of spike trains, refer to Harrison et al (2013); Brillinger (1988); Brown et al (2004); Kass et al (2005); West (2007); Reich et al (1998); Barbieri et al (2001); Kass and Ventura (2001); Grün et al (2002); Kass et al (2005); Rigat et al (2006); Patnaik et al (2008); Pillow et al (2008); Jacobs et al (2009); Diekman et al (2009); Sastry and Unnikrishnan (2010); Kottas et al (2012); Kelly and Kass (2012); Shahbaba et al (2014).…”

“…This is an important work, mainly because it offers a coherent approach for the hypothesis testing problem of the independence among multiple spike trains by utlizing generalized linear modeling. Shahbaba et al (2014) extended this work to multiple neurons by a semi-parametric Bayesian Model. The non-parametric Gaussian process model was proposed to estimate the time-varying firing probabilities while the parametric copula model accounted for the correlation structure among the multiple neurons.…”