Deep Fréchet Regression

2134 

Contributed Abstract 

Paper 

SU I IAO (1), Yidong Zhou (2), Hans-Georg Mueller (3)

(1) University of California, Davis, Davis, CA, (2) N/A, N/A, (3) UC Davis, N/A

Yidong Zhou  
N/A

Hans-Georg Mueller  
UC Davis

SU I IAO  
University of California, Davis

SU I IAO  
N/A

The paper introduces a pioneering solution by using the power of deep learning, drawing inspiration from manifold learning techniques. Our approach integrates low-dimensional representations derived from metric-space valued responses into a deep neural network. Complemented by local fréchet regression, this framework offers flexibility without imposing parametric assumptions on predictor-response relationships. The innovative amalgamation of techniques, incorporating manifold learning, deep neural networks, and local fréchet regression, positions our approach as a cutting-edge methodology poised to advance the field of regression analysis in the face of evolving data complexities and challenges. To establish a comprehensive theoretical framework, we first investigate the convergence rate of deep neural networks under dependent sub-Gaussian noises along with biases. The convergence rate of the proposed regression model is then obtained by expanding the scope of local fréchet regression to accommodate multivariate predictorsn within the framework of errors-in-variables regression. Through simulations and applications, the proposed model consistently outperforms existing approaches.

Curse of Dimensionality|Deep Learning|Fréchet regression|Non-Euclidean data|Manifold learning|

IMS

Statistical Methodology