Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models

We implement a pseudolikelyhood approach with l2-regularization as well as the recently introduced pseudolikelihood with decimation procedure to the inverse problem in continuous spin models on arbitrary networks, with arbitrarily disordered couplings. Performances of the approaches are tested against data produced by Monte Carlo numerical simulations and compared also from previously studied fully-connected mean-field-based inference techniques. The results clearly show that the best network reconstruction is obtained through the decimation scheme, that also allows to dwell the inference down to lower temperature regimes. Possible applications to phasor models for light propagation in random media are proposed and discussed.