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The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
A method is derived for estimating the nonparanormal, the method's theoretical properties are studied, and it is shown that it works well in many examples. Expand
High Dimensional Semiparametric Gaussian Copula Graphical Models
It is proved that the nonparanormal skeptic achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation, and this result suggests that the NonParanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Expand
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
The method has a clear interpretation: the authors use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling, which requires essentially no conditions. Expand
Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions
It is proved that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists and any limit point generated by SCGD is a stationary point, for which the convergence rate analysis is provided. Expand
Challenges of Big Data Analysis.
Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that areExpand
A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of highExpand
SpAM: Sparse Additive Models
A statistical analysis of the properties of SpAM and empirical results on synthetic and real data show that SpAM can be effective in fitting sparse nonparametric models in high dimensional data. Expand
The huge Package for High-dimensional Undirected Graph Estimation in R
An R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data and allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency. Expand
Blockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery
We develop a cyclical blockwise coordinate descent algorithm for the multi-task Lasso that efficiently solves problems with thousands of features and tasks. The main result shows that a closed-formExpand
A Strictly Contractive Peaceman-Rachford Splitting Method for Convex Programming
This paper focuses on the application of the Peaceman-Rachford splitting method to a convex minimization model with linear constraints and a separable objective function, and suggests attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and proposes a strictly contractive PRSM. Expand