In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[EX Q]: The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the ADADMM on a high-performance computer cluster by solving a large-scale logistic regression problem. Keywords Distributed optimization, ADMM, Asynchronous, Consensus optimization Tsung-Hui Chang is the corresponding author. Address: School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China 518172, E-mail: tsunghui.chang@ieee.org. Wei-Cheng Liao is with Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA, E-mail: mhong@umn.edu Mingyi Hong is with Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, 50011, USA, E-mail: mingyi@iastate.edu Xiangfeng Wang is with Shanghai Key Lab for Trustworthy Computing, Software Engineering Institute, East China Normal University, Shanghai, 200062, China, E-mail: xfwang@sei.ecnu.edu.cn September 10, 2015 DRAFT
[EX A]: Asynchronous Distributed ADMM for Large-Scale Optimization- Part II: Linear Convergence Analysis and Numerical Performance

[EX Q]: In many applications spanning from sensor to social networks, transportation systems, gene regulatory networks or big data, the signals of interest are defined over the vertices of a graph. The aim of this paper is to propose a least mean square (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.
[EX A]: Least Mean Squares Estimation of Graph Signals

[EX Q]: Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have succeeded in capturing word similarities as well as semantic and syntactic regularities. Instead, we aim at reviving interest in a model based on counts. We present a systematic study of the use of the Hellinger distance to extract semantic representations from the word co-occurrence statistics of large text corpora. We show that this distance gives good performance on word similarity and analogy tasks, with a proper type and size of context, and a dimensionality reduction based on a stochastic low-rank approximation. Besides being both simple and intuitive, this method also provides an encoding function which can be used to infer unseen words or phrases. This becomes a clear advantage compared to predictive models which must train these new words.
[EX A]:
Rehabilitation of Count-based Models for Word Vector Representations