Parallel Selective Algorithms for Big Data Optimization

We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. Our framework is very flexible and includes both fully parallel Jacobi schemes and Gauss- Seidel (i.e., sequential) ones, as well as virtually all possibilities "in between" with only a subset of variables updated at each iteration. Our theoretical convergence results improve on existing ones, and numerical results on LASSO, logistic regression, and some nonconvex quadratic problems show that the new method consistently outperforms existing algorithms.Comment: This work is an extended version of the conference paper that has been presented at IEEE ICASSP'14. The first and the second author contributed equally to the paper. This revised version contains new numerical results on non convex quadratic problem

The Family of MapReduce and Large Scale Data Processing Systems

In the last two decades, the continuous increase of computational power has produced an overwhelming flow of data which has called for a paradigm shift in the computing architecture and large scale data processing mechanisms. MapReduce is a simple and powerful programming model that enables easy development of scalable parallel applications to process vast amounts of data on large clusters of commodity machines. It isolates the application from the details of running a distributed program such as issues on data distribution, scheduling and fault tolerance. However, the original implementation of the MapReduce framework had some limitations that have been tackled by many research efforts in several followup works after its introduction. This article provides a comprehensive survey for a family of approaches and mechanisms of large scale data processing mechanisms that have been implemented based on the original idea of the MapReduce framework and are currently gaining a lot of momentum in both research and industrial communities. We also cover a set of introduced systems that have been implemented to provide declarative programming interfaces on top of the MapReduce framework. In addition, we review several large scale data processing systems that resemble some of the ideas of the MapReduce framework for different purposes and application scenarios. Finally, we discuss some of the future research directions for implementing the next generation of MapReduce-like solutions.Comment: arXiv admin note: text overlap with arXiv:1105.4252 by other author

An update on statistical boosting in biomedicine

Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely flexible, as the underlying base-learners (regression functions defining the type of effect for the explanatory variables) can be combined with any kind of loss function (target function to be optimized, defining the type of regression setting). In this review article, we highlight the most recent methodological developments on statistical boosting regarding variable selection, functional regression and advanced time-to-event modelling. Additionally, we provide a short overview on relevant applications of statistical boosting in biomedicine