The Complexity of Learning Verification

Informally, one branch of learning theory focuses on making statements of the form 'this learned classifier is at least X good'. A common intuition underlying many bounds of this form is that some form of 'prior' or 'bias' must exist on the set of all classifiers in order to make such statements. This intuition can be made precise in a few forms. I'll discuss the ways by which 'bias' and 'prior' allow verifiable learning as well as the limitations of 'prior' in addressing this problem.