  We theoretically analyze the typical learning performance of
$\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model
selection using the replica method from statistical mechanics. For typical
random regular graphs in the paramagnetic phase, an accurate estimate of the
typical sample complexity of $\ell_1$-LinR is obtained. Remarkably, despite the
model misspecification, $\ell_1$-LinR is model selection consistent with the
same order of sample complexity as $\ell_{1}$-regularized logistic regression
($\ell_1$-LogR), i.e., $M=\mathcal{O}\left(\log N\right)$, where $N$ is the
number of variables of the Ising model. Moreover, we provide an efficient
method to accurately predict the non-asymptotic behavior of $\ell_1$-LinR for
moderate $M, N$, such as precision and recall. Simulations show a fairly good
agreement between theoretical predictions and experimental results, even for
graphs with many loops, which supports our findings. Although this paper mainly
focuses on $\ell_1$-LinR, our method is readily applicable for precisely
characterizing the typical learning performances of a wide class of
$\ell_{1}$-regularized $M$-estimators including $\ell_1$-LogR and interaction
screening.

Machine Learning;Disordered Systems and Neural Networks;Artificial Intelligence;Machine Learning