Computing one-bit compressive sensing via double-sparsity constrained optimization

One-bit compressive sensing is popular in signal processing and communications due to the advantage of its low storage costs and hardware complexity. However, it has been a challenging task all along since only the one-bit (the sign) information is available to recover the signal. In this paper, we appropriately formulate the one-bit compressed sensing by a double-sparsity constrained optimization problem. The first-order optimality conditions via the newly introduced τ-stationarity for this nonconvex and discontinuous problem are established, based on which, a gradient projection subspace pursuit (GPSP) approach with global convergence and fast convergence rate is proposed. Numerical experiments against other leading solvers illustrate the high efficiency of our proposed algorithm in terms of the computation time and the quality of the signal recovery as well

Quadratic convergence of smoothing Newton's method for 0/1 loss optimization

It has been widely recognized that the 0/1-loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to the combinatorial nature of the 0/1 loss function, methods based on convex relaxations or smoothing approximations have dominated the existing research and are often able to provide approximate solutions of good quality. However, those methods are not optimizing the 0/1 loss function directly and hence no optimality has been established for the original problem. This paper aims to study the optimality conditions of the 0/1 function minimization and for the first time to develop Newton's method that directly optimizes the 0/1 function with a local quadratic convergence under reasonable conditions. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods

Quadratic convergence of Smoothing Newton's method for 0/1 loss optimization

It has been widely recognized that the 0/1 loss function is one of the most natural choices for modeling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to the combinatorial nature of the 0/1 loss function, methods based on convex relaxations or smoothing approximations have dominated the existing research and are often able to provide approximate solutions of good quality. However, those methods are not optimizing the 0/1 loss function directly and hence no optimality has been established for the original problem. This paper aims to study the optimality conditions of the 0/1 function minimization, and for the first time to develop Newton's method that directly optimizes the 0/1 function with a local quadratic convergence under reasonable conditions. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods

Deep Learning in Mobile and Wireless Networking: A Survey

The rapid uptake of mobile devices and the rising popularity of mobile applications and services pose unprecedented demands on mobile and wireless networking infrastructure. Upcoming 5G systems are evolving to support exploding mobile traffic volumes, agile management of network resource to maximize user experience, and extraction of fine-grained real-time analytics. Fulfilling these tasks is challenging, as mobile environments are increasingly complex, heterogeneous, and evolving. One potential solution is to resort to advanced machine learning techniques to help managing the rise in data volumes and algorithm-driven applications. The recent success of deep learning underpins new and powerful tools that tackle problems in this space. In this paper we bridge the gap between deep learning and mobile and wireless networking research, by presenting a comprehensive survey of the crossovers between the two areas. We first briefly introduce essential background and state-of-the-art in deep learning techniques with potential applications to networking. We then discuss several techniques and platforms that facilitate the efficient deployment of deep learning onto mobile systems. Subsequently, we provide an encyclopedic review of mobile and wireless networking research based on deep learning, which we categorize by different domains. Drawing from our experience, we discuss how to tailor deep learning to mobile environments. We complete this survey by pinpointing current challenges and open future directions for research

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page