Sunday, Aug 4: 2:35 PM - 2:50 PM
2134
Contributed Papers
Oregon Convention Center
This paper addresses the challenge of modeling the relationship between non-Euclidean responses and Euclidean predictors. We propose a regression model capable of handling high-dimensional predictors without parametric assumptions. Two key 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 we state the feasibility of mapping the metric space where responses reside to a low-dimensional Euclidean space using manifold learning. We introduce a reverse mapping approach, using local fréchet regression, to revert the low-dimensional representation back to the original metric space. To establish a comprehensive theoretical framework, we investigate the convergence rate of deep neural network under dependent and biased sub-Gaussian noise. The convergence rate of the proposed regression model is then obtained by expanding the scope of local fréchet regression to accommodate multivariate predictors in the presence of errors in predictors. We show in simulations and applications the proposed model outperforms existing methods.
Curse of Dimensionality
Deep Learning
Fréchet regression
Non-Euclidean data
Manifold learning
Main Sponsor
IMS