State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data

Abstract

Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.

Cell assemblies at multiple time scales with arbitrary lag constellations

“…$true0\overline{l}\equiv {\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}}_{l}false({\mathrm{\#}}_{AB,l}false)$. For deriving the proper distributional assumptions under the $true0H_0$, spike count series $\left\{c_{K,t}\right\}$ are often thresholded (Grün et al, 2002a; Humphries, 2011; Shimazaki et al, 2012; Picado-Muiño et al, 2013) such that binary {0,1}-series are obtained, presumably partially since multivariate extensions of the binomial or hypergeometric distribution are not yet commonplace (see Teugels, 1990; Dai et al, 2013). Especially for larger bin widths $true0\mathrm{normal\Delta }$ this implies a serious loss of information, however.…”

“…In another approach to synchronous spike-cluster detection based on the cumulants of the population spike density of all simultaneously recorded neurons, Staude et al (Staude et al, 2010a, 2010b) developed a method and stringent statistical test for checking the presence of higher-order (lag-0) correlations among neurons, without however providing the identity of the recorded assembly units. A recent ansatz by Shimazaki et al (Shimazaki et al, 2012) builds on a state-space model for Poisson point processes developed by Smith and Brown (Smith and Brown, 2003) to extract higher-order (lag-0) precise correlation patterns from multiple simultaneously recorded spike trains (see also (Pipa et al, 2008; Gansel and Singer, 2012; Picado-Muiño et al, 2013; Torre et al, 2013, 2016b; Billeh et al, 2014) for other recent approaches to the detection of groups of synchronous single spikes).Smith et al (Smith and Smith, 2006; Smith et al, 2010) address the problem of testing significance of recurring spike time sequences or activity chains like those observed in hippocampal place cells (Figure 1A, II, IV; see also [Abeles and Gerstein, 1988; Abeles and Gat, 2001; Lee and Wilson, 2004; Fujisawa et al, 2008; Gerstein et al, 2012]). Their approach makes use only of the order information in the neural activations, neglecting exact relative timing of spikes or even the number of spikes emitted by each neuron, in order to allow for derivation of exact probabilities based on the multinomial distribution and combinatorial considerations.…”

Sparse and low-rank matrix regularization for learning time-varying Markov networks

“…Another promising application of the time-varying MNs would be the analysis of multi-channel measurements of the brain activity, such as neuronal spike trains (Shimazaki et al 2012) or other brain imaging modalities like functional magnetic resonance imaging (fMRI) or magnetoencephalography (MEG). Interestingly, time-varying functional connectivity (dependency) between cortical regions has recently been a very active research target in the neuroscience and brain imaging communities (Hutchison 2013;Leonardi 2013).…”

Spatiotemporal Conditional Inference and Hypothesis Tests for Neural Ensemble Spiking Precision

“…Log-linear models are popular contemporary models for spike train data (Gerstein et al, 1989; Martignon et al, 1995; Vaadia et al, 1995; Martignon et al, 2000; Amari et al, 2003; Gütig et al., 2003; Schneidman et al, 2006; Shlens et al, 2006; Montani et al, 2009; Roudi et al, 2009; Truccolo et al, 2010; Kass et al, 2011; Long II and Carmena, 2011; Shimazaki et al, 2012). We begin with the abstract framework and then use special cases to build intuition.…”