Recent amplification of the North American winter temperature dipole.

During the winters of 2013-2014 and 2014-2015, anomalously warm temperatures in western North America and anomalously cool temperatures in eastern North America resulted in substantial human and environmental impacts. Motivated by the impacts of these concurrent temperature extremes and the intrinsic atmospheric linkage between weather conditions in the western and eastern United States, we investigate the occurrence of concurrent "warm-West/cool-East" surface temperature anomalies, which we call the "North American winter temperature dipole." We find that, historically, warm-West/cool-East dipole conditions have been associated with anomalous mid-tropospheric ridging over western North America and downstream troughing over eastern North America.

MINIMAX BOUNDS FOR SPARSE PCA WITH NOISY HIGH-DIMENSIONAL DATA.

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors.

Exact Covariance Thresholding into Connected Components for Large-Scale Graphical Lasso.

We consider the sparse inverse covariance regularization problem or with regularization parameter λ. Suppose the sample formed by thresholding the entries of the sample covariance matrix at λ is decomposed into connected components. We show that the induced by the connected components of the thresholded sample covariance graph (at λ) is equal to that induced by the connected components of the estimated concentration graph, obtained by solving the graphical lasso problem for the λ.