Ising Model Selection Using ℓ_1-Regularized Linear Regression
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We theoretically investigate the performance of ℓ_1-regularized linear regression (ℓ_1-LinR) for the problem of Ising model selection using the replica method from statistical mechanics. The regular random graph is considered under paramagnetic assumption. Our results show that despite model misspecification, the ℓ_1-LinR estimator can successfully recover the graph structure of the Ising model with N variables using M=𝒪(log N) samples, which is of the same order as that of ℓ_1-regularized logistic regression. Moreover, we provide a computationally efficient method to accurately predict the non-asymptotic performance of the ℓ_1-LinR estimator with moderate M and N. Simulations show an excellent agreement between theoretical predictions and experimental results, which supports our findings.
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