B0248
Title: High-dimensional measurement error models for Lipschitz losses with application to functional connectivity
Authors: Xin Ma - Columbia University (United States) [presenting]
Suprateek Kundu - The University of Texas at MD Anderson Cancer Center (United States)
Abstract: Recently emerged biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors of the data features create potential difficulties for statistical estimation and feature selection. There are limited existing measurement error models involving high-dimensional covariates, which usually require knowledge of the noise distribution and typically focus on linear or generalized linear models. The high-dimensional measurement error models are extended to a broader class of loss functions with Lipschitz continuity without the requirement of noise distribution. A Lasso analogue version of the method is subsequently proposed that is computationally scalable to much higher dimensions. Theoretical guarantees are derived even when the number of covariates increases exponentially with the sample size. Extensive simulation studies demonstrate superior performance compared to existing methods in classification and quantile regression problems. The approach is applied to a gender classification task based on functional connectivity and significant network edges are identified that reveal gender differences.
