Core Concepts
This paper introduces novel methods for multivariate linear regression when responses are highly correlated, focusing on sparse regression coefficient estimation and efficient computation even with a dense error covariance matrix.
Stats
The study uses a training set of 50 observations and a test set of 200 observations.
The authors experiment with different dimensions for predictors (p) and responses (q), including (20, 50), (50, 20), and (80, 80).
Sparsity levels of the regression coefficient matrix are controlled by parameters s1 and s2, with values ranging from 0.1 to 1.
The equicorrelation parameter (θ) in the error covariance matrix varies from 0 to 0.95.
The study considers both constant and heterogeneous marginal error variances (ηi).
Performance is evaluated using metrics like model error, prediction error, true negative rate (TNR), and true positive rate (TPR).