En las fronteras de la Materia Condensada

The statistical learning theory is a probabilistic theory. It considers systems capable of learning, i.e. to adapt to the environment based on samples of environmental data. The paradigm of learning theory is data classification or pattern recognition (like medical diagnosis, manuscript characters recognition, etc). If the examples are previously classified (by an expert), learning is called "supervised". If the classifiaction is based only on regularities of the data detected by the learner itself, learning is "unsupervised". The aim is to give correct answers -to classify correctly- new incoming signals not previously used for learning. This property is called generalization. The theory allows to determine under which conditions generalization is possible. Statistical physics considers the same framework, and predicts the typical generalization performance on well defined tasks in the limit of a large number of high dimensional data. Depending on the the type of problem and on the learning algorithm, the existence of phase transitions of second and first order between low-performance and high-performance learning phases have been discovered. We review some recent results obtained with the statistical mechanics approach, and discuss some open questions.