  In this Letter we propose a new method to infer the topology of the
interaction network in pairwise models with Ising variables. By using the
pseudolikelihood method (PLM) at high temperature, it is generally possible to
distinguish between zero and nonzero couplings because a clear gap separate the
two groups. However at lower temperatures the PLM is much less effective and
the result depends on subjective choices, such as the value of the $\ell_1$
regularizer and that of the threshold to separate nonzero couplings from null
ones. We introduce a decimation procedure based on the PLM that recursively
sets to zero the less significant couplings, until the variation of the
pseudolikelihood signals that relevant couplings are being removed. The new
method is fully automated and does not require any subjective choice by the
user. 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 spin
glasses). These numerical results show that the new algorithm performs better
than standard PLM

Disordered Systems and Neural Networks;Statistical Mechanics