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In this Letter we propose a new method to infer the topology of theinteraction network in pairwise models with Ising variables. By using thepseudolikelihood method (PLM) at high temperature, it is generally possible todistinguish between zero and nonzero couplings because a clear gap separate thetwo groups. However at lower temperatures the PLM is much less effective andthe result depends on subjective choices, such as the value of the $\ell_1$regularizer and that of the threshold to separate nonzero couplings from nullones. We introduce a decimation procedure based on the PLM that recursivelysets to zero the less significant couplings, until the variation of thepseudolikelihood signals that relevant couplings are being removed. The newmethod is fully automated and does not require any subjective choice by theuser. Numerical tests have been performed on a wide class of Ising models,having different topologies (from random graphs to finite dimensional lattices)and different couplings (both diluted ferromagnets in a field and spinglasses). These numerical results show that the new algorithm performs betterthan standard PLM

Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models