Algorithm 2 P-GLASSO Algorithm

Initialize W = diag(S) + λI, and Θ = W−1. Cycle around the columns repeatedly, performing the following steps till convergence: Rearrange the rows/columns so that the target column is last (implicitly). Compute ${\mathbf{\Theta }}_{11}^{-1}$ using (3.3). Solve (3.1) for α, using as warm starts the solution from the previous round of row/column updates. Update ${\widehat{\mathit{\theta }}}_{12}=\widehat{\mathit{\alpha }}/w_{22}$, and ${\widehat{\theta }}_{22}$ using (3.2). Update Θ and W using (2.6), ensuring that ΘW = Ip. Output the solution Θ (precision) and its exact inverse W (covariance).