EconPapers    
Economics at your fingertips  
 

Large-scale linear regression: Development of high-performance routines

Alvaro Frank, Diego Fabregat-Traver and Paolo Bientinesi

Applied Mathematics and Computation, 2016, vol. 275, issue C, 411-421

Abstract: In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding datasets occupy terabytes of disk space. As the availability of large-scale datasets increases regularly, so does the challenge in dealing with them. Indeed, traditional solvers—which rely on the use of “black-box” routines optimized for one single OLS—are highly inefficient and fail to provide a viable solution for big-data analyses. As a case study, in this paper we consider a linear regression consisting of two-dimensional grids of related OLS problems that arise in the context of genome-wide association analyses, and give a careful walkthrough for the development of ols-grid, a high-performance routine for shared-memory architectures; analogous steps are relevant for tailoring OLS solvers to other applications. In particular, we first illustrate the design of efficient algorithms that exploit the structure of the OLS problems and eliminate redundant computations; then, we show how to effectively deal with datasets that do not fit in main memory; finally, we discuss how to cast the computation in terms of efficient kernels and how to achieve scalability. Importantly, each design decision along the way is justified by simple performance models. ols-grid enables the solution of 1011 correlated OLS problems operating on terabytes of data in a matter of hours.

Keywords: Linear regression; Ordinary least squares; Algorithm design; Out-of-core; Parallelism; Scalability (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315015805
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:275:y:2016:i:c:p:411-421

DOI: 10.1016/j.amc.2015.11.078

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-03-19
Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:411-421