Abstract
We statistically characterize the population spiking activity obtained from simultaneous recordings of neurons across all layers of a cortical microcolumn. Three types of models are compared: an Ising model which captures pairwise correlations between units, a Restricted Boltzmann Machine (RBM) which allows for modeling of higher-order correlations, and a semi-Restricted Boltzmann Machine which is a combination of Ising and RBM models. Model parameters were estimated in a fast and efficient manner using minimum probability flow, and log likelihoods were compared using annealed importance sampling. The higher-order models reveal localized activity patterns which reflect the laminar organization of neurons within a cortical column. The higher-order models also outperformed the Ising model in log-likelihood: On populations of 20 cells, the RBM had 10% higher log-likelihood (relative to an independent model) than a pairwise model, increasing to 45% gain in a larger network with 100 spatiotemporal elements, consisting of 10 neurons over 10 time steps. We further removed the need to model stimulus-induced correlations by incorporating a peri-stimulus time histogram term, in which case the higher order models continued to perform best. These results demonstrate the importance of higher-order interactions to describe the structure of correlated activity in cortical networks. Boltzmann Machines with hidden units provide a succinct and effective way to capture these dependencies without increasing the difficulty of model estimation and evaluation.
Highlights
Electrophysiology is rapidly moving towards high density recording techniques capable of capturing the simultaneous activity of large populations of neurons
Modeling laminar population recordings We estimated Ising, Restricted Boltzmann Machine (RBM) and semi-Restricted Boltzmann Machine (sRBM) models for populations of cortical cells simultaneously recorded across all cortical layers in a microcolumn of cat V1 in response to long, continuous natural movies presented at a frame rate of 150 Hz
The RBM provides a parsimonious model for higher-order dependencies in neural population data
Summary
Electrophysiology is rapidly moving towards high density recording techniques capable of capturing the simultaneous activity of large populations of neurons. This raises the challenge of understanding how networks encode and process information in ways that go beyond tuning properties or feedforward receptive field models. The Ising model, originally developed in the 1920s to describe magnetic interactions [1], has been used to statistically characterize electrophysiological data, in the retina [2], and more recently for cortical recordings [3,4] This model treats spikes from a population of neurons binned in time as binary vectors and captures dependencies between cells with the maximum entropy distribution for pairwise dependencies. This has been shown to provide a good model for small groups of cells in the retina [5], though it is unable to capture dependencies higher than second-order
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