A0589
Title: Deep Frechet regression
Authors: Yidong Zhou - University of California, Davis (United States) [presenting]
Su I Iao - University of California Davis (United States)
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. The challenge of modeling relationships is addressed between non-Euclidean responses and multivariate Euclidean predictors. A flexible regression model is proposed, capable of handling high-dimensional predictors without imposing parametric assumptions. Two primary challenges are addressed: the curse of dimensionality in nonparametric regression and the absence of linear structure in general metric spaces. The former is tackled using deep neural networks, while for the latter, the feasibility of mapping the metric space is demonstrated where responses reside to a low-dimensional Euclidean space using manifold learning. A reverse mapping approach is introduced, employing local Frechet regression to map the low-dimensional manifold representations back to objects in the original metric space. A theoretical framework is developed, investigating the convergence rate of deep neural networks under dependent sub-Gaussian noise with bias. The convergence rate of the proposed regression model is then obtained by expanding the scope of local Frechet regression to accommodate multivariate predictors in the presence of errors in predictors. Simulations and case studies show that the proposed model outperforms existing methods for non-Euclidean responses, focusing on the special cases of probability measures and networks.
