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.

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
Asynchronous Distributed ADMM for Large-Scale Optimization- Part II: Linear Convergence Analysis and Numerical Performance

This paper presents generalized probabilistic models for high-order projective dependency parsing and an algorithmic framework for learning these statistical models involving dependency trees. Partition functions and marginals for high-order dependency trees can be computed efficiently, by adapting our algorithms which extend the inside-outside algorithm to higher-order cases. To show the effectiveness of our algorithms, we perform experiments on three languages English, Chinese and Czech, using maximum conditional likelihood estimation for model training and L-BFGS for parameter estimation. Our methods achieve competitive performance for English, and outperform all previously reported dependency parsers for Chinese and Czech.
Probabilistic Models for High-Order Projective Dependency Parsing

We present a visually grounded model of speech perception which projects spoken utterances and images to a joint semantic space. We use a multi-layer recurrent highway network to model the temporal nature of spoken speech, and show that it learns to extract both form and meaningbased linguistic knowledge from the input signal. We carry out an in-depth analysis of the representations used by different components of the trained model and show that encoding of semantic aspects tends to become richer as we go up the hierarchy of layers, whereas encoding of formrelated aspects of the language input tends to initially increase and then plateau or decrease.
Representations of language in a model of visually grounded speech signal