Towards the Validation of Inductive Learning Systems

The present paper deals with inductive inference of recur-sive functions, in general, and with the problem of validating inductive learning devices, in particular. Thus, the paper aims at a contribution to the research and development area of intelligent systems validation. As those systems are typically interactive and, therefore, utilized in open loops of human{machine interactions, the problem of their validity is substantially complicated. A certain family of validation scenarios is adopted. Within this framework , we ask for the power and the limitations of these validation approaches. The expertise necessary and suucient to accomplish successful validation is of some particular interest. One of the key questions is for the comparison of domain expertise and validation expertise. The area of inductive inference of recursive functions is taken as a case for complex interactive systems validation. Computability theory is providing a rich source of theoretical concepts and results suitable for the focused investigations. Emphasis is put on explicating the importance of abstract computational complexity, limiting computability, and relativized computability. These concepts are exploited for characterizing the expertise necessary and suucient in the validation of inductive inference systems. Particular emphasis is put on relating validation expertise and domain expertise by means of rela-tivized computability concepts. One of the key results on validation of inductive learning systems exhibits that validation expertise necessarily implies the expertise for solving the focused learning problems. 1 Motivation The focus of the present paper is on inductive inference systems, but we draw a particular motivation from another area: complex interactive systems validation. u There is an obvious necessity to validate and verify complex systems, respectively. It might easily happen that :::the inability to adequately evaluate systems may become the limiting factor in our ability to employ systems that our technology and knowledge will allow us to design. (cf. 12])