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

Lotfi Slim, Clément Chatelain, Chloe-Agathe Azencott, Jean-Philippe Vert
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5857-5865, 2019.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-slim19a, title = {kernel{PSI}: a Post-Selection Inference Framework for Nonlinear Variable Selection}, author = {Slim, Lotfi and Chatelain, Cl{\'e}ment and Azencott, Chloe-Agathe and Vert, Jean-Philippe}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5857--5865}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/slim19a/slim19a.pdf}, url = {https://proceedings.mlr.press/v97/slim19a.html}, 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.} }
Endnote
%0 Conference Paper %T kernelPSI: a Post-Selection Inference Framework for Nonlinear Variable Selection %A Lotfi Slim %A Clément Chatelain %A Chloe-Agathe Azencott %A Jean-Philippe Vert %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-slim19a %I PMLR %P 5857--5865 %U https://proceedings.mlr.press/v97/slim19a.html %V 97 %X 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.
APA
Slim, L., Chatelain, C., Azencott, C. & Vert, J.. (2019). kernelPSI: a Post-Selection Inference Framework for Nonlinear Variable Selection. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5857-5865 Available from https://proceedings.mlr.press/v97/slim19a.html.

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