= Paired group Lasso optimality conditions
{title2=$g=0:\ \|c\|_2\leq\lambda;\qquad g\ne0:\ c=\lambda g/\|g\|_2$}
For each unordered pair, $g=(\Theta_{jk},\Theta_{kj})$ and $c=(X_j^{\mathsf T}r_k/n,X_k^{\mathsf T}r_j/n)$ with centred columns and <regression residuals>. The <subdifferential> of the <Euclidean norm> is the unit ball at zero and $g/\|g\|_2$ otherwise. These <KKT conditions> are necessary and sufficient for the convex paired objective and explain joint edge deletion.
Back to article page
