3The Structural Risk Minimization principle on set-valued probability space

Statistical learning theory (SLT) based on random samples on probability space is considered as the best theory about small samples statistics learning at present and has become a new hot field in machine learning after neural networks. However, the theory can not handle the small samples statistical learning problems on set-valued probability space which widely exists in real world. In this paper, Borel-Cantelli lemma based on random sets is proven on set-valued probability space. The structural risk minimization (SRM) based on random sets samples on set-valued probability space is established.