Penalized Splines and Reproducing Kernel Methods

Abstract

Two data analytic research areas—penalized splines and reproducing kernel methods—have become very vibrant since the mid-1990s. This article shows how the former can be embedded in the latter via theory for reproducing kernel Hilbert spaces. This connection facilitates cross-fertilization between the two bodies of research. In particular, connections between support vector machines and penalized splines are established. These allow for significant reductions in computational complexity, and easier incorporation of special structure such as additivity.

KEY WORDS :

• Bioinformatics
• Classification
• Data mining
• Generalized additive models
• Kernel machines
• Machine learning
• Mixed models
• Reproducing kernel hilbert spaces
• Semi-parametric regression
• Statistical learning
• Supervised learning
• Support vector machines