Advancement of micro-electro-mechanics and wireless communication have proliferated the deployment of large-scale wireless sensor networks. Due to cost, size and power constraints, at most a few sensor nodes can be equipped with a global positioning system; such nodes (whose positions can be accurately determined) are referred to as anchors. However, one can deter-mine the distance between two nearby sensors using some form of local communication. The problem of computing the positions of the non-anchor nodes from the inter-sensor distances and anchor positions is referred as sensor network localization (SNL). In this dissertation, our aim is to develop an accurate, efficient, and scalable localization algorithm, which can operate both in the presence and absence of anchors. It has been demon-strated in the literature that divide-and-conquer approaches can be used to localize large net-works without compromising the localization accuracy. The core idea with such approaches is to partition the network into overlapping subnetworks, localize each subnetwork using the available distances (and anchor positions), and finally register the subnetworks in a single coordinate system. In this regard, the contributions of this dissertation are as follows: We study the global registration problem and formulate a necessary “rigidity” condition for uniquely recovering the global sensor locations. In particular, we present a method for efficiently testing rigidity, and a heuristic for augmenting the partitioned network to enforce rigidity. We present a mechanism for partitioning the network into smaller subnetworks using cliques. Each clique is efficiently localized using multidimensional scaling. Finally, we use a recently proposed semidefinite program (SDP) to register the localized subnetworks. We develop a scalable ADMM solver for the SDP in question. We present simulation results on random and structured networks to demonstrate the pro-posed methods perform better than state-of-the-art methods in terms of run-time, accuracy, and scalability.

<p>In this work, we study a class of Markovian information theoretic optimization problems motivated by the recent interests in incorporating mutual information as performance metrics which gives evident success in representation learning, feature extraction and clustering problems. In particular, we focus on the information bottleneck (IB) and privacy funnel (PF) methods and their recent multi-view, multi-source generalizations that gain attention because the performance significantly improved with multi-view, multi-source data. Nonetheless, the generalized problems challenge existing IB and PF solves in terms of the complexity and their abilities to tackle large-scale data. </p> <p>To address this, we study both the IB and PF under a unified framework and propose solving it through splitting methods, including renowned algorithms such as alternating directional method of multiplier (ADMM), Peaceman-Rachford splitting (PRS) and Douglas-Rachford splitting (DRS) as special cases. Our convergence analysis and the locally linear rate of convergence results give rise to new splitting method based IB and PF solvers that can be easily generalized to multi-view IB, multi-source PF. We implement the proposed methods with gradient descent and empirically evaluate the new solvers in both synthetic and real-world datasets. Our numerical results demonstrate improved performance over the state-of-the-art approach with significant reduction in complexity. Furthermore, we consider the practical scenario where there is distribution mismatch between training and testing data generating processes under a known bounded divergence constraint. In analyzing the generalization error, we develop new techniques inspired by the input-output mutual information approach and tighten the existing generalization error bounds.</p>