Representations of cortical activity using Restricted Boltzmann Machine

Restricted Boltzmann Machines (RBM) are neural network models that learn a probability distribution and a representation of data, they belong to the class of Boltzmann Machines. With respect to the lasts, in RBM the learning procedure is simpler and faster. Furthermore, once properly trained, final couplings will directly show the main correlations between visible units. In this work we apply RBM to a specific cortical neural data set and demonstrate its usefulness in revealing important properties of this brain region. Starting from the studies of A. Peyrache et al. on medial Prefrontal Cortex's neural activity in a rat, in which, using simple PCA, a cell assembly coding for a particular learned rule was found, we tried to reproduce their result, deepen the description of such phenomenon. G. Tavoni et al. have shown that an Ising model can faithful reproduce such activity quite well, improving what a simple PCA is able to attain. This suggests a possible efficacy of Boltzmann machines, and then of RBM, since they are equivalent to an Ising model. Even though good results were obtained, the limitations of Kullback-Leibler Divergence in such contest forced us to modify the learning rule: in fact, RBM training is based on the principle of Maximal Likelihood Expectation, equivalent to minimization of such divergence. This is the reason why we redefined our machinery using a metric coming from optimal transport theory called the Wasserstein distance, instead of Kullback-Liebler divergence, that has the virtues to be smoother and finite in cases where the previous one, conversely, diverges. The success of the project could represent a simple way to analyze bigger datasets of neural activity measurements, speeding up the research in this field, both for a fast analysis and a simple, graphical representation of the learning mechanisms taking place in the brain.