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

TL;DR

This paper compares regularization and decimation pseudolikelihood methods for inferring XY-spin models, demonstrating that decimation yields superior network reconstruction, especially at lower temperatures, with potential applications in light propagation in random media.

Contribution

It introduces and tests decimation pseudolikelihood inference for XY-spin models, showing its advantages over regularization and mean-field methods in network reconstruction.

Findings

Decimation approach outperforms regularization in network inference.

Decimation maintains accuracy at lower temperatures.

Method applicable to models of light propagation in random media.

Abstract

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.