The growth in the use of computationally intensive statistical procedures, especially with Big Data, has necessitated the usage of parallel computation on diverse platforms such as multicore, GPU, clusters and clouds. However, slowdown due to interprocess communication costs typically limits such methods to "embarrassingly parallel" (EP) algorithms, especially on non-shared memory platforms. This paper develops a broadly-applicable method for converting many non-EP algorithms into statistically equivalent EP ones. The method is shown to yield excellent levels of speedup for a variety of statistical computations. It also overcomes certain problems of memory limitations.
@cite_9: Spandex having good whiteness retention, high heat-set efficiency, and percent set is made from comprises amide soluble polyurethaneurea polymers prepared by reacting polyether which comprises the reaction product of a polymeric glycols with ortho-substituted diisocyanates and bulky diamine chain extenders.
@cite_10: D&R is a new statistical approach to the analysis of large complex data. The data are divided into subsets. Computationally, each subset is a small dataset. Analytic methods are applied to each of the subsets, and the outputs of each method are recombined to form a result for the entire data. Computations can be run in parallel with no communication among them, making them embarrassingly parallel, the simplest possible parallel processing. Using D&R, a data analyst can apply almost any statistical or visualization method to large complex data. Direct application of most analytic methods to the entire data is either infeasible, or impractical. D&R enables deep analysis: comprehensive analysis, including visualization of the detailed data, that minimizes the risk of losing important information. One of our D&R research thrusts uses statistics to develop “best” division and recombination procedures for analytic methods. Another is a D&R computational environment that has two widely used components, R and Hadoop, and our RHIPE merger of them. Hadoop is a distributed database and parallel compute engine that executes the embarrassingly parallel D&R computations across a cluster. RHIPE allows analysis wholly from within R, making programming with the data very efficient. Copyright © 2012 John Wiley & Sons, Ltd.
@cite_9 developed a variant of CA, essentially what will be called C without the A'' in Section , with the goal of speedup. Some of the same authors did some finite-sample analysis of CA in the linear regression case in @cite_10 .