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Abstract:
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Kernel regression has become an essential tool in modeling nonlinear effect of high-dimensional features. However, constructing a valid and powerful hypothesis testing procedure for the interaction between feature groups remains difficult in practice. The main challenges arise from the difficulty in correctly estimating the null model when the functional form of feature effect is unknown. This work addresses this challenge by proposing Cross-validated Kernel Ensemble (CKE), that learns the space of appropriate functions for a particular dataset using an ensemble-based approach. Using a library of kernels, CKE automatically estimates the form of the kernel functions from the data, resulting in a test that is robust against model misspecification and have improved power. We evaluate the finite-sample performance of our approach to that of other popular methods under a set of realistic nutrition-environment interaction models, and finally demonstrate the application of our method on real data.
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