Linear regression models have been successfully used to function estimation and model selection in high-dimensional data analysis. However, most existing methods are built on least squares with the mean square error (MSE) criterion, which are sensitive to outliers and their performance may be degraded for heavy-tailed noise. In this paper, we go beyond this criterion by investigating the regularized modal regression from a statistical learning viewpoint. A new regularized modal regression model is proposed for estimation and variable selection, which is robust to outliers, heavy-tailed noise, and skewed noise. On the theoretical side, we establish the approximation estimate for learning the conditional mode function, the sparsity analysis for variable selection, and the robustness characterization. On the application side, we applied our model to successfully improve the cognitive impairment prediction using the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort data.
|Number of pages||11|
|Journal||Advances in Neural Information Processing Systems|
|Publication status||Published - 2017|
|Event||31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States|
Duration: 2017 Dec 4 → 2017 Dec 9
Bibliographical noteFunding Information:
This work was partially supported by U.S. NSF-IIS 1302675, NSF-IIS 1344152, NSF-DBI 1356628, NSF-IIS 1619308, NSF-IIS 1633753, NIH AG049371. Hong Chen was partially supported by National Natural Science Foundation of China (NSFC) 11671161. We are grateful to the anonymous NIPS reviewers for the insightful comments.
© 2017 Neural information processing systems foundation. All rights reserved.
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing