A0421
Title: Tensor additive quantile regression
Authors: Wenqi Lu - Nankai University (China) [presenting]
Abstract: Additive nonparametric models are increasingly favored for analyzing tensor data, offering a flexible and parsimonious approach. A tensor additive quantile regression model is introduced, aiming to provide a more robust and detailed understanding of how covariates influence the response in tensor data. The component functions are estimated using basis function approximations. The splines are stacked as an additional tensor dimension, which allows the leverage of the tensor structure, and Tucker decomposition is applied for dimension reduction. In high-dimensional settings, a sparse tensor additive quantile regression model that incorporates a group penalty for variable selection is proposed. A key challenge addressed is connecting sparse tensor elements within the structure of Tucker decomposition. An innovative approach is proposed that identifies a broader set of relevant features than the oracle while enabling efficient algorithms to navigate the high-dimensional space. The large sample properties of the proposed estimators is established, the finite sample performance of the method is evaluated through Monte Carlo simulations, and its application is demonstrated on real-world datasets, including stock market and head pose image data.
