Stationary-Sparse Causality Network Learning
Yuejia He, Yiyuan She, Dapeng Wu.
Year: 2013, Volume: 14, Issue: 94, Pages: 3073−3104
Abstract
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 $\mathbf{S}^2$ 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.