1 Unsupervised learning

Our last model that uses unsupervised learning is again a general learning machine invented by Geoffrey Hinton and Terrance Sejnowski in the mid 1980 called Boltzmann machine. This machine is a general form of a recurrent neural network with visible nodes that receive input or provide output, and hidden notes that are not connected to the outside world directly. Such a stochastic dynamic network, a recurrent system with hidden nodes, together with the adjustable connections, provide the system with enough degrees of freedom to approximate any dynamical system. While this has been recognized for a long time, finding practical training rules for such systems have been a major challenge for which there was only recently major progress. These machines use unsupervised learning to learn hierarchical representations based on the statistics of the world. Such representations are key to more advanced applications of machine learning and to human abilities. The basic building block is a one-layer network with one visible layer and one hidden layer. An example of such a network is shown in Fig. 1.1. The nodes represent random variable similar to the Bayesian networks discussed before. We will specifically consider binary nodes that mimic neuronal states which are either firing or not. The connections between the have weights wij which specify how much they influence the on-state of connected nodes. Such systems can be described by an energy function. The energy between two nodes that are symmetrically connected with strength wij is