SMURC: High-Dimension Small-Sample Multivariate Regression With Covariance Estimation

作者：Bayar Belhassen^*; Bouaynaya Nidhal; Shterenberg Roman

来源：IEEE Journal of Biomedical and Health Informatics, 2017, 21(2): 573-581.

DOI：10.1109/JBHI.2016.2515993

• High-dimension low sample size
• multivariate regression
• maximum likelihood (ML)
• gene regulatory network

We consider a high-dimension low samplesize multivariate regression problem that accounts for correlation of the response variables. The system is underdetermined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a normalization of the likelihood function that guarantees convergence. We call this method small-sample multivariate regression with covariance (SMURC) estimation. We derive an optimization problem and its convex approximation to compute SMURC. Simulation results show that the proposed algorithm outperforms the regularized likelihood estimator with known covariance matrix and the sparse conditional Gaussian graphical model. We also apply SMURC to the inference of the wing-muscle gene network of the Drosophila melanogaster (fruit fly).

• 出版日期2017-3