期刊
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
卷 143, 期 11, 页码 1835-1858出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jspi.2013.05.019
关键词
Canonical correlation; Group Lasso; Hierarchical clustering; High-dimensional inference; Lasso; Oracle inequality; Variable screening; Variable selection
资金
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1106753, 0906420] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1209014] Funding Source: National Science Foundation
We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso based on the structure from the clusters. Regarding the first step, we present a novel and bottom-up agglomerative clustering algorithm based on canonical correlations, and we show that it finds an optimal solution and is statistically consistent. We also present some theoretical arguments that canonical correlation based clustering leads to a better-posed compatibility constant for the design matrix which ensures identifiability and an oracle inequality for the group Lasso. Furthermore, we discuss circumstances where cluster-representatives and using the Lasso as subsequent estimator leads to improved results for prediction and detection of variables. We complement the theoretical analysis with various empirical results. (C) 2013 Elsevier B.V. All rights reserved.
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