https://hal-cea.archives-ouvertes.fr/cea-01586170Marruzzo, AlessiaAlessiaMarruzzoCINECA [Bologna]Tyagi, PayalPayalTyagiS.Li.M. Lab - Soft and Living Matter Laboratory - NANOTEC - CNR Istituto di Nanotecnologia - CNR - Consiglio Nazionale delle Ricerche [Roma]Antenucci, FabrizioFabrizioAntenucciIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiquePagnani, AndreaAndreaPagnaniPolito - Politecnico di Torino = Polytechnic of Turin Leuzzi, LucaLucaLeuzziUOS Rome - IPCF-CNRImproved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous VariablesHAL CCSD2017[PHYS.PHYS.PHYS-DATA-AN] Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an][PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]De Laborderie, Emmanuelle2017-09-12 15:19:592023-03-24 14:53:052017-09-12 15:19:59enPreprints, Working Papers, ...1We propose and test improvements to state-of-the-art techniques of Bayesian statistical inference based on pseudolikelihood maximization with $\ell_1$ regularization and with decimation. In particular, we present a method to determine the best value of the regularizer parameter starting from a hypothesis testing technique. Concerning the decimation, we also analyze the worst case scenario's in which there is no sharp peak in the tilded-pseudolikelihood function, firstly defined as a criterion to stop the decimation. Techniques are applied to noisy systems with non-linear dynamics, mapped onto multi-variable interacting Hamiltonian effective models for waves and phasors. Results are analyzed varying the number of available samples and the externally tunable temperature-like parameter mimicking real data noise. Eventually the behavior of inference procedures described are tested against a wrong hypothesis: non-linearly generated data are analyzed with a pairwise interacting hypothesis. Our analysis shows that, looking at the behavior of the inverse graphical problem as data size increases, the methods exposed allow to rule out a wrong hypothesis.