Modeling Higher-Order Correlations within Cortical Microcolumns

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.Author Summary: Communication between neurons underlies all perception and cognition. Hence, to understand how the brain's sensory systems such as the visual cortex work, we need to model how neurons encode and communicate information about the world. To this end, we simultaneously recorded the activity of many neurons in a cortical column, a fundamental building block of information processing in the brain. This allows us to discover statistical structure in their activity, a first step to uncovering communication pathways and coding principles. To capture the statistical structure of firing patterns, we fit models that assign a probability to each observed pattern. Fitting probability distributions is generally difficult because the model probabilities of all possible states have to sum to one, and enumerating all possible states in a large system is not possible. Making use of recent advances in parameter estimation, we are able to fit models and test the quality of the fit to the data. The resulting model parameters can be interpreted as the effective connectivity between groups of cells, thus revealing patterns of interaction between neurons in a cortical circuit.