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kernelPSI: a Post-Selection Inference Framework for Nonlinear Variable Selection

Abstract : Model selection is an essential task for many applications in scientific discovery. The most common approaches rely on univariate linear measures of association between each feature and the outcome. Such classical selection procedures fail to take into account nonlinear effects and interactions between features. Kernel-based selection procedures have been proposed as a solution. However, current strategies for kernel selection fail to measure the significance of a joint model constructed through the combination of the basis kernels. In the present work, we exploit recent advances in post-selection inference to propose a valid statistical test for the association of a joint model of the selected kernels with the outcome. The kernels are selected via a step-wise procedure which we model as a succession of quadratic constraints in the outcome variable.
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Submitted on : Wednesday, January 15, 2020 - 4:58:40 PM
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  • HAL Id : hal-02441304, version 1


Lotfi Slim, Clement Chatelain, Chloé-Agathe Azencott, Jean-Philippe Vert. kernelPSI: a Post-Selection Inference Framework for Nonlinear Variable Selection. 36th International Conference on Machine Learning (ICML 2019), Jun 2019, Long Beach, CA, United States. ⟨hal-02441304⟩



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