Incremental proximal methods for large scale convex optimization

Laboratory for Information and Decision Systems Report LIDS-P-2847We consider the minimization of a sum∑m [over]i=1 fi (x) consisting of a large number of convex component functions fi . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components.We also discuss applications in a few contexts, including signal processing and inference/machine learning.United States. Air Force Office of Scientific Research (grant FA9550-10-1-0412

Compressed RF Tomography for Wireless Sensor Networks: Centralized and Decentralized Approaches

Abstract. Radio Frequency (RF) tomography refers to the process of inferring information about an environment by capturing and analyzing RF signals trans-mitted between nodes in a wireless sensor network. In the case where few avail-able measurements are available, the inference techniques applied in previous work may not be feasible. Under certain assumptions, compressed sensing tech-niques can accurately infer environment characteristics even from a small set of measurements. This paper introduces Compressed RF Tomography, an approach that combines RF tomography and compressed sensing for monitoring in a wire-less sensor network. We also present decentralized techniques which allow mon-itoring and data analysis to be performed cooperatively by the nodes. The sim-plicity of our approach makes it attractive for sensor networks. Experiments with simulated and real data demonstrate the capabilities of the approach in both cen-tralized and decentralized scenarios.