Ising model selection using ℓ ₁-regularized linear regression: a statistical mechanics analysis*

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