B1139
Title: Frechet sufficient dimension reduction and variable selection
Authors: Jiaying Weng - Bentley University (United States) [presenting]
Abstract: Studying non-Euclidean objects has gained significant momentum with the proliferation of advanced data acquisition techniques and the rise of sophisticated modeling approaches. Researchers now recognize the immense potential of analyzing and understanding data that deviates from the traditional Euclidean framework. The focus is on the sparse Frechet problem, where the predictor dimension is much larger than the sample size. A multitask regression is constructed using artificial response variables from the leading eigenvectors of a weighted inverse regression ensemble matrix to estimate the central subspace. This construction's benefit is avoiding calculating the inverse of a large covariance matrix and easily implementing penalization to achieve sparse estimation. A minimax concave penalty is incorporated into the constructed multitask regression to eliminate estimation biases, further improving variable selection. To solve the nonconvex optimization problem, a novel local double approximation algorithm is proposed, approximating the loss function and the penalty term, respectively, resulting in explicit expressions in each iteration. The proposed algorithm performs superior to existing approaches through extensive numerical studies and real data analysis.
