Functional ANOVA Models: Convex-concave approach and concurvity analysis
نویسندگان
چکیده
This paper aims at bridging a gap between functional ANOVA modeling and recent advances in machine learning and kernel-based models. Functional ANOVA on the one hand extends linear ANOVA techniques to nonlinear multivariate models as smoothing splines, aiming to provide interpretability to an estimate and handling the curse of dimensionality. Multiple kernel learning (MKL) on the other hand is well studied in a context of machine learning, Support Vector Machines (SVMs) and kernel-based modeling. Its goal is to combine different sources of information into a powerful predictive model. This paper points to conceptual and computational relations of both frameworks: a first result is the integration of RBF kernels into a formal tensor product space suitable for functional ANOVA models. From a computational perspective, COSSO as proposed in nonparametric statistics is found to fit a framework of convex-concave programming. A main theme is that the occurrence of concurvity obstructs the interpretation of the models studied in both frameworks.
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