Accelerated Consensus via Min-Sum Splitting

We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to the problem solution. We prove that a proper choice of the tuning parameters allows Min-Sum Splitting to yield subdiffusive accelerated convergence rates, matching the rates obtained by shift-register methods. The acceleration scheme embodied by Min-Sum Splitting for the consensus problem bears similarities with lifted Markov chains techniques and with multi-step first order methods in convex optimization

Privacy-preserving model learning on a blockchain network-of-networks.

ObjectiveTo facilitate clinical/genomic/biomedical research, constructing generalizable predictive models using cross-institutional methods while protecting privacy is imperative. However, state-of-the-art methods assume a "flattened" topology, while real-world research networks may consist of "network-of-networks" which can imply practical issues including training on small data for rare diseases/conditions, prioritizing locally trained models, and maintaining models for each level of the hierarchy. In this study, we focus on developing a hierarchical approach to inherit the benefits of the privacy-preserving methods, retain the advantages of adopting blockchain, and address practical concerns on a research network-of-networks.Materials and methodsWe propose a framework to combine level-wise model learning, blockchain-based model dissemination, and a novel hierarchical consensus algorithm for model ensemble. We developed an example implementation HierarchicalChain (hierarchical privacy-preserving modeling on blockchain), evaluated it on 3 healthcare/genomic datasets, as well as compared its predictive correctness, learning iteration, and execution time with a state-of-the-art method designed for flattened network topology.ResultsHierarchicalChain improves the predictive correctness for small training datasets and provides comparable correctness results with the competing method with higher learning iteration and similar per-iteration execution time, inherits the benefits of the privacy-preserving learning and advantages of blockchain technology, and immutable records models for each level.DiscussionHierarchicalChain is independent of the core privacy-preserving learning method, as well as of the underlying blockchain platform. Further studies are warranted for various types of network topology, complex data, and privacy concerns.ConclusionWe demonstrated the potential of utilizing the information from the hierarchical network-of-networks topology to improve prediction

Distributed Deblurring of Large Images of Wide Field-Of-View

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images.Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processin

A Distributed Newton Method for Network Utility Maximization

Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newton-type fast converging algorithm for solving network utility maximization problems with self-concordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes in a decentralized manner with limited information exchange. Similarly, the stepsize can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the stepsize in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition.Comment: 27 pages, 4 figures, LIDS report, submitted to CDC 201