Generalization in learning from examples

Vera Kůrková

pp. 343-363

in: Włodzisław Duch, Jacek Mańdziuk (eds), Challenges for computational intelligence, Berlin, Springer, 2007

Abstract

Capability of generalization in learning from examples can be modeled using regularization, which has been developed as a tool for improving stability of solutions of inverse problems. Theory of inverse problems has been developed to solve various tasks in applied science such as acoustics, geophysics and computerized tomography. Such problems are typically described by integral operators. It is shown that learning from examples can be reformulated as an inverse problem defined by an evaluation operator. This reformulation allows one to characterize optimal solutions of learning tasks and design learning algorithms based on numerical solutions of systems of linear equations.