Statistical modelling of higher-order correlations in pools of neural activity

Abstract

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2 N − 1)-dimensional model for a population with N neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from high-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of high-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.

Ensemble inhibition and excitation in the human cortex: An Ising-model analysis with uncertainties

“…The addition of higher-order moments as constraints has the potential to improve the model [27,[30][31][32][33]91], especially since input nonlinearities have been argued to affect beyond-pairwise correlations [12,26]. However, even the inclusion of three-point functions already results in a model with O(N 3 ) parameters, which requires significantly more data points to avoid overfitting.…”

“…Despite Ising models' success in describing the statistics of spiking patterns, they also have certain limitations. First, it has been argued that higher-order neuron couplings could play an important role in population coding, so that pairwise couplings fail to capture the full dynamics [25][26][27][28][29][30][31][32][33], especially if exact spike timing is important [34,35]. Second, the model's reliability may be distance-dependent, leading to successful predictions for neurons separated by large distances, but poor fits to the activity of local clusters of neurons that might be dominated by high-order correlations due to distance dependent connectivity profiles [28,36,37].…”

Characterization of Visuomotor/Imaginary Movements in EEG: An Information Theory and Complex Network Approach

“…The information is transmitted through trains of action potential or less frequently by local field potentials (LFPs). More specifically for the action potentials, the information can also be transmitted through the counting of spikes, the temporal precision of them, the structure of the time series, the synchronization between groups of neurons, or some combination of these [1][2][3][4][5][6][7][8][9][10][11]. Thus, the brain does not have a single code but multiple which depend on multiple complex dynamic variables.…”

Uncovering Network Architecture Using an Exact Statistical Input-Output Relation of a Neuron Model

“…The aim of this study is to make a link between network architecture and statistics of neural activity through nonlinearity of the input-output relation of the neurons. Several studies of higher-order interactions among model neurons reveal key features of neural activity, and suggest mechanisms underlying the observed interactions in a neural pool (Cayco-Gajic et al, 2015;Montangie and Montani, 2017;Montani et al, 2013;Shimazaki et al, 2015;Zylberberg and Shea-Brown, 2015). But since strong synapses shape the backbone of network architecture, a model that accurately include nonlinear behavior of such synapses, is essential to reveal network architecture.…”