  We propose an efficient strategy to infer sparse Hopfield network based on
magnetizations and pairwise correlations measured through Glauber samplings.
This strategy incorporates the $\ell_{1}$ regularization into the Bethe
approximation by a quadratic approximation to the log-likelihood, and is able
to further reduce the inference error of the Bethe approximation without the
regularization. The optimal regularization parameter is observed to be of the
order of $M^{-\nu}$ where $M$ is the number of independent samples. The value
of the scaling exponent depends on the performance measure. $\nu\simeq0.5001$
for root mean squared error measure while $\nu\simeq0.2743$ for
misclassification rate measure. The efficiency of this strategy is demonstrated
for the sparse Hopfield model, but the method is generally applicable to other
diluted mean field models. In particular, it is simple in implementation
without heavy computational cost.
