Lasso sign recovery from cone invertibility
= Lasso sign recovery from cone invertibility
{c}
Suppose every $\delta$ in the <Lasso cone condition> satisfies $\psi\|\delta_S\|_\infty\leq\|\widehat\Sigma\delta\|_\infty$. On the usual score event, the <Karush-Kuhn-Tucker conditions> give $\|\widehat\Sigma(\widehat\beta-\beta^0)\|_\infty\leq3\lambda/2$. Hence every active-coordinate error is at most $3\lambda/(2\psi)$, and a larger minimum nonzero signal guarantees coordinatewise sign recovery.