This thesis investigates a new training technique for Restricted Boltzmann Machines (RBMs), a type of stochastic neural network employed in unsupervised learning. Specifically, the focus of this work is on RBMs with a Gaussian prior distribution for the hidden units, leading to a training technique that depends exclusively on the visible units provided as input. The method relies on Expectation Propagation (EP), a Bayesian inference technique designed to approximate intractable distributions. As a testing ground, we analyze its performance on the MNIST dataset, a large database of handwritten digits commonly used for training and testing machine learning algorithms. First, we begin by detailing the historical background and the foundational concepts of RBMs, followed by a similar exposition for EP.