= Prediction inequality from Lasso stationarity
{title2=$\|X\delta\|_2^2/n\leq\eta^TX\delta/n+\lambda(\|\beta^0\|_1-\|\widehat\beta\|_1)$}
For <Lasso> loss $\|Y-X\beta\|_2^2/(2n)+\lambda\|\beta\|_1$ and $Y=X\beta^0+\eta$, stationarity with a penalty <subgradient> gives $\|X\delta\|_2^2/n\leq\eta^TX\delta/n+\lambda(\|\beta^0\|_1-\|\widehat\beta\|_1)$, $\delta=\widehat\beta-\beta^0$. This follows by multiplying the <Karush-Kuhn-Tucker conditions> by $\delta$ and using $z^T\widehat\beta=\|\widehat\beta\|_1$ and $z^T\beta^0\leq\|\beta^0\|_1$.
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