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We introduce an algorithm which, in the context of nonlinear regression onvector-valued explanatory variables, chooses those combinations of vectorcomponents that provide best prediction. The algorithm devotes particularattention to components that might be of relatively little predictive value bythemselves, and so might be ignored by more conventional methodology for modelchoice, but which, in combination with other difficult-to-find components, canbe particularly beneficial for prediction. Additionally the algorithm avoidschoosing vector components that become redundant once appropriate combinationsof other, more relevant components are selected. It is suitable for very highdimensional problems, where it keeps computational labour in check by using anovel sequential argument, and also for more conventional prediction problems,where dimension is relatively low. We explore properties of the algorithm usingboth theoretical and numerical arguments.

An Algorithm for Nonlinear, Nonparametric Model Choice and Prediction