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High-dimensional Nonparanormal Graph Estimation via Smooth-projected Neighborhood Pursuit
Tuo Zhao · Kathryn Roeder · Han Liu

Mon Dec 03 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor
We propose a new smooth-projected neighborhood pursuit method for estimating high dimensional undirected graphs. Our method can be viewed as a semiparametric extension of the popular neighborhood pursuit approach proposed by N. Meinshausen and P. B{ü}hlmann 2006 from Gaussian to Gaussian copula models (or the nonparanormal models as proposed by Liu et. al 2009). In terms of methodology and computation, we project a possibly indefinite symmetric matrix into the cone of positive semidefinite matrices. The projection is formulated as a smoothed element-wise $\ell_\infty$-norm minimization problem. We develop an efficient fast proximal gradient algorithm with a provable optimal rate of convergence $\cO(1/\sqrt{\epsilon})$, where $\epsilon$ is the desired accuracy for the objective value. In terms of theory, we provide an alternative view to analyze the trade-off between computational efficiency and statistical error. We give a sufficient condition to secure that the smooth-projected neighborhood pursuit estimator achieves graph estimation consistency. Empirically, we conduct real data experiments on stock and genomic datasets to illustrate the usefulness of the proposed method.

Author Information

Tuo Zhao (Johns Hopkins University Princeton University)
Kathryn Roeder (Carnegie Mellon University)
Han Liu (Tencent AI Lab)

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