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_14: In the past decades, we have witnessed a revolution in information technology. Routine collection of systematically generated data is now commonplace. Databases with hundreds of fields (variables), and billions of records (observations) are not unusual. This presents a difficulty for classical data analysis methods, mainly due to the limitation of computer memory and computational costs (in time, for example). In this paper, we propose an intelligent regression analysis methodology which is suitable for modeling massive datasets. The basic idea here is to split the entire dataset into several blocks, applying the classical regression techniques for data in each block, and finally combining these regression results via weighted averages. Theoretical justification of the goodness of the proposed method is given, and empirical performance based on extensive simulation study is discussed.
Chunked estimation was then investigated in another special case, that of linear regression, in @cite_14 , motivated by memory requirement problems rather than speed. The authors allowed their chunk averaging to be weighted, and they derived the optimal weights. They also showed that certain statistics would be @math distributed under the assumption of normally-distributed populations, and studied the resulting chunked estimators via simulation. However, that work was restricted to linear regression, not general types of estimators, and was not aimed at parallel processing, i.e. speedup.