Poisson's equation for discrete-time quasi-birth-and-death processes

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix. We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value

Accelerated Variance Reduced Stochastic ADMM

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T) as opposed to O(1/T^2) of accelerated batch algorithms, where $T$ is the number of iterations. Thus, there still remains a gap in convergence rates between existing stochastic ADMM and batch algorithms. To bridge this gap, we introduce the momentum acceleration trick for batch optimization into the stochastic variance reduced gradient based ADMM (SVRG-ADMM), which leads to an accelerated (ASVRG-ADMM) method. Then we design two different momentum term update rules for strongly convex and general convex cases. We prove that ASVRG-ADMM converges linearly for strongly convex problems. Besides having a low per-iteration complexity as existing stochastic ADMM methods, ASVRG-ADMM improves the convergence rate on general convex problems from O(1/T) to O(1/T^2). Our experimental results show the effectiveness of ASVRG-ADMM.Comment: 16 pages, 5 figures, Appears in Proceedings of the 31th AAAI Conference on Artificial Intelligence (AAAI), San Francisco, California, USA, pp. 2287--2293, 201

Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization

The Schatten-p quasi-norm $(0<p<1)$ is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we first define two tractable Schatten quasi-norms, i.e., the Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively, which lead to the design of very efficient algorithms that only need to update two much smaller factor matrices. We also design two efficient proximal alternating linearized minimization algorithms for solving representative matrix completion problems. Finally, we provide the global convergence and performance guarantees for our algorithms, which have better convergence properties than existing algorithms. Experimental results on synthetic and real-world data show that our algorithms are more accurate than the state-of-the-art methods, and are orders of magnitude faster.Comment: 16 pages, 5 figures, Appears in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), Phoenix, Arizona, USA, pp. 2016--2022, 201

A Chinese perspective on Western coverage of China past and present

What would a 21st century Chinese media student make of a documentary about Nixon’s historic trip to China back in 1972? What would they think of former CNN correspondent Mike Chinoy’s view that Nixon colluded with China’s propaganda spin? And what they make of the view in this review of the film, that the Chinese government is still locked into that mentality of using the media for its own ends? LSE media student Yuanyuan Liu gives her view