A0438
Title: Inference on derivatives of high-dimensional regression function with deep neural networks (NN)
Authors: Weining Wang - University of Groningen (Netherlands) [presenting]
Abstract: The purpose is to study the estimation of the partial derivatives of non-parametric regression functions with many predictors and a subsequent significance test for the said derivatives. The derivative estimator is the derivative of the convolution of a regression function estimator and a smoothing kernel, where the regression function estimator is a deep neural network whose structure could scale up as the sample size grows. It is demonstrated that in the context of modeling with deep neural networks, derivative estimation is quite different from estimating the regression function itself, and hence the smoothing operation becomes beneficial and even necessary. The subsequent significance test, where the null hypothesis is that a partial derivative is zero, is based on the moment-generating function of the aforementioned derivative estimator. This test finds applications in model specification and variable screening for high-dimensional data. To render the estimator and test effective when facing predictors with high or even diverging dimensions, it is assumed that first, the observed high-dimensional predictors can effectively serve as the proxies for certain latent, lower-dimensional factors and that second, only the latent factors and a subset of the coordinates of the observed high-dimensional predictors drive the regression function.
