Variable Selection with Rigorous Uncertainty Quantification using Deep Bayesian Neural Networks: Posterior Concentration and Bernstein-von Mises Phenomenon

3 Dec 2019Jeremiah Zhe Liu

This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable importance effectively in high dimensions, and its learning rate can sometimes "break" the curse of dimensionality... (read more)

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