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

Belhassen Bayar, Nidhal Bouaynaya, Roman Shterenberg

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider a high-dimension low sample-size 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).

Original languageEnglish (US)
Article number7377009
Pages (from-to)573-581
Number of pages9
JournalIEEE Journal of Biomedical and Health Informatics
Issue number2
StatePublished - Mar 2017

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Health Information Management


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