A further discussion of structural risk minimization principle on set-valued probability space

Statistical Learning Theory (SLT) based on random samples on probability space is considered as an important theory about small samples statistics learning at present and has become a new field in machine learning after neural networks. However, the theory is difficult to handle the small samples statistical learning problems on set-valued probability space which widely exists in real world. In this paper utilizing the partial relation “≤” and the properties of set-valued probability, Borel-Cantelli lemma based on random sets is revisited on set-valued probability space, then the Structural Risk Minimization (SRM) principle based on random sets samples on set-valued probability space is reestablished.