New research harnesses the powers of single value decomposition (SVD) and sparse learning to tackle the problem of inferring relationships between predictors and responses in large-scale, high-dimensional datasets.
Addressing problems in computation speed, assumptions of scarcity, and algorithm sensitivity
One major challenge that statisticians face when inferring relationships is that modern data is big and the underlying true relationships between predictors and responses are sparse and multilayered. To quickly establish connections in these datasets, Ma et al. utilize a combination of SVD and sparse learning, called thresholding SVD (T-SVD). This new algorithm solves many issues that plagued the Statistics and Big Data communities, such as the problems of computation speed, the assumption of sparcity, and the sensitivity of the algorithm to positive results. In their simulation study, T-SVD is shown to be better in relation to speed and sensitivity than existing methods such as the sequential extraction algorithm (SEA) and the iterative exclusive extraction algorithm (IEEA). As a result, the multilayered relationships between predictors and responses, which come in the form of multidimensional matrices, can be learned quickly and accurately.
Uncovering new regulatory networks
Demonstrating the application of T-SVD, Ma et al. showed that new biological insights can be gained from using T-SVD to analyze datasets from The Cancer Genome Atlas consortium. The authors focused on the ovarian cancer gene expression datasets, in which the sample size is much smaller than the number of regulators and responses measured in the study. As in a typical genomic experiment, tens of thousands of genes were probed for their expression levels; from pathway studies, we know that very few of these genes form control switches that govern the expression levels for the rest of the genome. Ma et al. inferred two different relationships, based on microRNA (miRNA) or long noncoding RNA (lncRNA). The authors showed that these regulatory relationships specifically match established cancer pathways very well. Geneticists now have two new regulatory networks to mine for understanding the roles of miRNAs and lncRNAs.
In short, T-SVD is an exciting algorithm that pushes the Statistics field forward by offering a new lens to look at large-scale multidimensional datasets. With this approach, statisticians and users of statistics, like geneticists, can gain new insights into existing datasets and tackle new research problems.
Ma, Xin, Luo Xiao, Wing Hung Wong. Learning regulatory programs by threshold SVD regression. Proc Natl Acad SCI USA. 2014 Nov 4; 111 (44). DOI 10.1073/pnas.1417808111