On the Conditions of the VC Theory for Statistical Learning Applied to the Evaluation of Models for Complex Systems

摘要

This paper looks at the VC theory for statistical learning as a tool to analyze the uncertainty that underlies the behavior of complex dynamic systems. First, explanations as to why such a tool is needed are presented. Then, the results of the VC theory are summarized and presented in the form of two inequalities with the corresponding conditions on which they are based. These two inequalities are then compared. It is shown that they coincide asymptotically. A relationship between the parameters that define the conditions is proposed. For the case of smaller sample sizes, a numerical example is presented to examine the inequalities and determine which inequality is more conservative.