Consistency of Empirical Risk Minimization for Unbounded Loss Functions

The theoretical framework of Statistical Learning Theory (SLT) for pattern recognition problems is extended to comprehend the situations where an infinite value of the loss function is employed to prevent misclassifications in specific regions with high reliability. Sufficient conditions for ensuring the consistency of the Empirical Risk Minimization (ERM) criterion are then established and an explicit bound, in terms of the VC dimension of the class of decision functions employed to solve the problem, is derived.