title: Modeling higher-order correlations within cortical microcolumns.
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.
authors.affiliation: Redwood Center for Theoretical Neuroscience, University of California, Berkeley, Berkeley, California, United States of America.
authors.forename: Urs
authors.initials: U
authors.lastname: Köster
authors.affiliation: Department of Applied Physics, Stanford University and Khan Academy, Palo Alto, California, United States of America.
authors.forename: Jascha
authors.initials: J
authors.lastname: Sohl-Dickstein
authors.affiliation: Department of Cell Biology and Neuroscience, Montana State University, Bozeman, Montana, United States of America.
authors.forename: Charles M
authors.initials: CM
authors.lastname: Gray
authors.affiliation: Redwood Center for Theoretical Neuroscience, University of California, Berkeley, Berkeley, California, United States of America.
authors.forename: Bruno A
authors.initials: BA
authors.lastname: Olshausen
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D002415:Cats; D016000:Cluster Analysis; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D010775:Photic Stimulation; D014793:Visual Cortex / Q000502:physiology*