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# Adaptive Randomized Dimension Reduction on Massive Data

## Author(s): Darnell, Gregory; Georgiev, Stoyan; Mukherjee, Sayan; Engelhardt, Barbara E

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dc.contributor.authorDarnell, Gregory-
dc.contributor.authorGeorgiev, Stoyan-
dc.contributor.authorMukherjee, Sayan-
dc.contributor.authorEngelhardt, Barbara E-
dc.date.accessioned2021-10-08T19:48:42Z-
dc.date.available2021-10-08T19:48:42Z-
dc.date.issued2017en_US
dc.identifier.citationDarnell, Gregory, Stoyan Georgiev, Sayan Mukherjee, and Barbara E. Engelhardt. "Adaptive Randomized Dimension Reduction on Massive Data." The Journal of Machine Learning Research 18, no. 140 (2017): pp. 1-30.en_US
dc.identifier.urihttps://www.jmlr.org/papers/volume18/15-143/15-143.pdf-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1bv8z-
dc.description.abstractThe scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper, we develop an approach for dimension reduction that exploits the assumption of low rank structure in high dimensional data to gain both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide an efficient solution to principal component analysis (PCA), and we use this efficient solver to improve estimation in large- scale linear mixed models (LMM) for association mapping in statistical genomics. A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance by implicitly regularizing the covariance matrix estimate of the random effect in an LMM. These statistical and computational advantages are highlighted in our experiments on simulated data and large-scale genomic studies.en_US
dc.format.extent1 - 30en_US
dc.language.isoen_USen_US
dc.relation.ispartofJournal of Machine Learning Researchen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleAdaptive Randomized Dimension Reduction on Massive Dataen_US
dc.typeJournal Articleen_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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