Robust Sparse Estimation of Multi-Response Regression

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xinwei Deng*+ and Aurelie Lozano and Huijing Jiang
• Companies: Virginia Tech and IBM and IBM T.J. Watson Research Center
• Keywords: multi-response ; robustness ; joint modeling ; covariance matrix

Abstract

We propose a robust framework to jointly perform two critical tasks of high dimensional modeling in synergy: (i) learning a sparse functional mapping from multiple predictors to multiple responses while taking advantage of the coupling among responses, and (ii) estimating the conditional dependency structure among the responses while adjusting for their predictors. The traditional likelihood-based estimators lack resilience with respect to outliers and model misspecification. This issue is exacerbated when dealing with high dimensional noisy data. We therefore adopt an alternative approach to minimizing a regularized distance criterion, which is motivated by minimum distance estimators used in nonparametric methods. The proposed method yields an efficient algorithm that alternates between weighted versions of lasso and graphical lasso, where the sample weights intuitively explain the robustness of our method. We demonstrate the value of our framework through extensive simulation and real eQTL data analysis.