Distance Matrix Estimation from Noisy Observation of Low Rank Position Matrix

• Activity Number: 311
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Zijian Guo* and Tony Cai
• Companies: University of Pennsylvania and University of Pennsylvania
• Keywords: Distance Matrix ; Low Rank Matrix ; Quadratic Functional ; Denoising ; SVD

Abstract

In a growing number of applications, we must estimate the distance matrix in a high dimensional setting. Observing $n$ points in high dimensional space $\R^{p}$, it is of interest to estimate the $n\times n$ distance matrix, whose elements are the pairwise distances between the points. By assuming the points lie in a low-dimensional space and using a projection, we develop an estimator of the distance matrix. We establish the error bound of our estimator, which matches the minimax lower bound. We conduct simulation studies and illustrate the good performance of the proposed estimator.