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Basics of Multivariate Analysis in Neuroimaging Data
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Sparse Multivariate Regression With Covariance Estimation.

Adam J Rothman1, Elizaveta Levina1, Ji Zhu1

  • 1Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1107.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|June 26, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new method for multivariate regression with covariance estimation (MRCE) to handle correlated responses. MRCE outperforms other methods, especially with high correlation, and is available in an R-package.

Keywords:
High dimension low sample sizeLassoMultiple output regressionSparsity

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Multivariate regression models are crucial for analyzing relationships between multiple response variables.
  • Accounting for correlations among response variables is essential for accurate statistical inference.
  • Existing methods may not effectively handle the complexity of simultaneous coefficient and covariance estimation.

Purpose of the Study:

  • To introduce a novel sparse estimator for multivariate regression coefficient matrices.
  • To develop a method that simultaneously estimates regression coefficients and the covariance structure.
  • To provide an efficient computational approach for the proposed method.

Main Methods:

  • The proposed method, multivariate regression with covariance estimation (MRCE), utilizes penalized likelihood.
  • Simultaneous estimation of regression coefficients and the covariance matrix is performed.
  • An efficient optimization algorithm and a fast approximation are developed for computation.

Main Results:

  • Simulation studies demonstrate that MRCE outperforms competing methods, particularly when response variables are highly correlated.
  • The method was successfully applied to a finance dataset for predicting asset returns.
  • An R-package with code and data is available for public use.

Conclusions:

  • MRCE offers a robust approach for sparse multivariate regression with correlated responses.
  • The method provides improved performance in scenarios with high inter-response correlation.
  • The availability of an R-package facilitates the adoption and application of MRCE in research and practice.