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We develop a simple and unified framework for nonlinear variable selectionthat incorporates uncertainty in the prediction function and is compatible witha wide range of machine learning models (e.g., tree ensembles, kernel methods,neural networks, etc). In particular, for a learned nonlinear model$f(\mathbf{x})$, we consider quantifying the importance of an input variable$\mathbf{x}^j$ using the integrated partial derivative $\Psi_j = \Vert\frac{\partial}{\partial \mathbf{x}^j} f(\mathbf{x})\Vert^2_{P_\mathcal{X}}$.We then (1) provide a principled approach for quantifying variable selectionuncertainty by deriving its posterior distribution, and (2) show that theapproach is generalizable even to non-differentiable models such as treeensembles. Rigorous Bayesian nonparametric theorems are derived to guaranteethe posterior consistency and asymptotic uncertainty of the proposed approach.Extensive simulations and experiments on healthcare benchmark datasets confirmthat the proposed algorithm outperforms existing classic and recent variableselection methods.

Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guarantees