Purpose – The purpose of this paper is to introduce some basic knowledge of statistical learning theory (SLT) based on random set samples in set‐valued probability space for the first time and generalize the key theorem and bounds on the rate of uniform convergence of learning theory in Vapnik, to the key theorem and bounds on the rate of uniform convergence for random sets in set‐valued probability space. SLT based on random samples formed in probability space is considered, at present, as one of the fundamental theories about small samples statistical learning. It has become a novel and important field of machine learning, along with other concepts and architectures such as neural networks. However, the theory hardly handles statistical learning problems for samples that involve random set samples.Design/methodology/approach – Being motivated by some applications, in this paper a SLT is developed based on random set samples. First, a certain law of large numbers for random sets is proved. Second, the de...

Some theoretical results of learning theory based on random sets in set‐valued probability space

Fil: Amicarelli, Adriana Natacha. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - San Juan. Instituto de Automatica. Universidad Nacional de San Juan. Facultad de Ingenieria. Instituto de Automatica; Argentina

Substrate Feeding Strategy Integrated with a Biomass Bayesian Estimator for a Biotechnological Process

Presents a qualitative introduction and justification of the application of statistical learning theory to uncertainty modeling in business and engineering systems. Using simple mathematical tools and metaphorical images, the main variables that govern the uncertainty in a physical system are defined. A general expression of uncertainty models is then obtained. The structure of this expression is the same as that of the uncertainty models that have been developed by rigorously applying the results of statistical learning theory.

A. Aziz Guergachi

Papers

Using statistical learning theory for modeling the uncertainty in business and engineering systems: a qualitative introduction