SIAM Journal on Matrix Analysis and Applications
On the projected subgradient method for nonsmooth convex optimization in a Hilbert space
Mathematical Programming: Series A and B
Convex Optimization
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
SIAM Journal on Optimization
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Subset selection for vector autoregressive processes using Lasso
Computational Statistics & Data Analysis
Network Science: Theory and Applications
Network Science: Theory and Applications
New Introduction to Multiple Time Series Analysis
New Introduction to Multiple Time Series Analysis
Ultrahigh Dimensional Feature Selection: Beyond The Linear Model
The Journal of Machine Learning Research
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Topology Selection in Graphical Models of Autoregressive Processes
The Journal of Machine Learning Research
Foundations and Trends® in Machine Learning
Computational Statistics & Data Analysis
IEEE Transactions on Information Theory
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Recently, researchers have proposed penalized maximum likelihood to identify network topology underlying a dynamical system modeled by multivariate time series. The time series of interest are assumed to be stationary, but this restriction is never taken into consideration by existing estimation methods. Moreover, practical problems of interest may have ultra-high dimensionality and obvious node collinearity. In addition, none of the available algorithms provides a probabilistic measure of the uncertainty for the obtained network topology which is informative in reliable network identification. The main purpose of this paper is to tackle these challenging issues. We propose the S2 learning framework, which stands for stationary-sparse network learning. We propose a novel algorithm referred to as the Berhu iterative sparsity pursuit with stationarity (BISPS), where the Berhu regularization can improve the Lasso in detection and estimation. The algorithm is extremely easy to implement, efficient in computation and has a theoretical guarantee to converge to a global optimum. We also incorporate a screening technique into BISPS to tackle ultra-high dimensional problems and enhance computational efficiency. Furthermore, a stationary bootstrap technique is applied to provide connection occurring frequency for reliable topology learning. Experiments show that our method can achieve stationary and sparse causality network learning and is scalable for high-dimensional problems.