TY - JOUR
T1 - Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation
AU - Zhao, Tuo
AU - Roeder, Kathryn
AU - Liu, Han
N1 - Funding Information:
Tuo Zhao and Han Liu are supported by NSF Grant III-1116730, while Kathryn Roeder was supported by National Institute of Mental Health Grant MH057881 (PI Bernie Devlin).
Publisher Copyright:
© 2014, © 2014 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
PY - 2014/10/25
Y1 - 2014/10/25
N2 - Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.
AB - Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.
KW - Graphical model
KW - High-dimensional statistics
KW - Model selection/Variable selection
KW - Multivariate analysis
KW - Numerical optimization
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U2 - 10.1080/10618600.2013.858633
DO - 10.1080/10618600.2013.858633
M3 - Article
C2 - 25382957
AN - SCOPUS:84908071840
SN - 1061-8600
VL - 23
SP - 895
EP - 922
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
IS - 4
ER -