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Feature selection in high-dimensional classification

Author(s): Kolar, Mladen; Liu, Han

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Abstract: High-dimensional discriminant analysis is of fundamental importance in multivariate statistics. Existing theoretical results sharply characterize different procedures, providing sharp convergence results for the classification risk, as well as the l2 convergence results to the discriminative rule. However, sharp theoretical results for the problem of variable selection have not been established, even though model interpretation is of importance in many scientific domains. In this paper, we bridge this gap by providing sharp sufficient conditions for consistent variable selection using the ROAD estimator (Fan et al., 2010). Our results provide novel theoretical insights for the ROAD estimator. Sufficient conditions are complemented by the necessary information theoretic limits on variable selection in high-dimensional discriminant analysis. This complementary result also establishes optimality of the ROAD estimator for a certain family of problems.
Publication Date: 2013
Citation: Kolar, Mladen, and Han Liu. "Feature selection in high-dimensional classification." Proceedings of the 30th International Conference on Machine Learning, (2013): pp. 329-337. Retrieved from
ISSN: 2640-3498
Pages: 329 - 337
Type of Material: Conference Article
Series/Report no.: Proceedings of Machine Learning Research;
Journal/Proceeding Title: Proceedings of the 30th International Conference on Machine Learning
Version: Final published version. This is an open access article.

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