2013 RobustSparseEstimationofMultire

• (Lozano et al., 2013) ⇒ Aurelie C. Lozano, Huijing Jiang, and Xinwei Deng. (2013). “Robust Sparse Estimation of Multiresponse Regression and Inverse Covariance Matrix via the L2 Distance.” In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ISBN:978-1-4503-2174-7 doi:10.1145/2487575.2487667

Subject Headings:

Cited By

• http://scholar.google.com/scholar?q=%222013%22+Robust+Sparse+Estimation+of+Multiresponse+Regression+and+Inverse+Covariance+Matrix+via+the+L2+Distance
• http://dl.acm.org/citation.cfm?id=2487575.2487667&preflayout=flat#citedby

Quotes

Author Keywords

• High dimensional data; inverse covariance; l2e; learning; multiresponse regression; robust estimation; sparse learning; variable selection

Abstract

We propose a robust framework to jointly perform two key modeling tasks involving high dimensional data: (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 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. In this work, we propose instead to minimize a regularized distance criterion, which is motivated by the minimum distance functionals used in nonparametric methods for their excellent robustness properties. The proposed estimates can be obtained efficiently by leveraging a sequential quadratic programming algorithm. We provide theoretical justification such as estimation consistency for the proposed estimator. Additionally, we shed light on the robustness of our estimator through its linearization, which yields a combination of weighted lasso and graphical lasso with the sample weights providing an intuitive explanation of the robustness. We demonstrate the merits of our framework through simulation study and the analysis of real financial and genetics data.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2013 RobustSparseEstimationofMultire	Aurelie C. Lozano Huijing Jiang Xinwei Deng			Robust Sparse Estimation of Multiresponse Regression and Inverse Covariance Matrix via the L2 Distance				10.1145/2487575.2487667		2013