A0968
Title: Inference on derivatives of high dimensional regression function with deep neural network
Authors: Yue Zhao - University of York (United Kingdom) [presenting]
Abstract: We study the estimation of the partial derivatives of non-parametric regression functions with many predictors, and a subsequent significance test for the said derivatives. Our 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. We demonstrate that in the context of modeling with deep neural networks, derivative estimation is quite different from estimating the regression function itself, and the smoothing operation becomes beneficial. Our 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. To render our estimator and test effective when in high dimensions, we assume that the high-dimensional predictors can serve as the proxies for certain latent, lower-dimensional factors; moreover, we estimate and test the partial derivatives in a coordinate-wise manner, similar to a screening procedure, after controlling for the latent factors. We also finely adjust the regression function estimator to achieve the desired asymptotic normality under the null hypothesis. We demonstrate the excellent performance of our test in a simulation study and real world applications. This is a joint work with Prof. Jianqing Fan at Princeton and Prof. Weining Wang at Groningen.
