2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217047On-line learning of probability distributions is analyzed from the field theoretical point of view. We can obtain an optimal on-line learning algorithm, since renormalization group enables us to control the number of degrees of freedom of a system according to the number of examples. We do not learn parameters of a model, but probability distributions themselves. Therefore, the algorithm requires no a priori knowledge of a model.4 pages, 1 figure, RevTexDisordered Systems and Neural NetworksAdaptation and Self-Organizing SystemsHigh Energy Physics - TheoryData Analysis, Statistics and Probabilitytext