Improved pseudolikelihood regularization and decimation methods on non-linearly interacting systems with continuous variables

• Main Author: Alessia Marruzzo, Payal Tyagi, Fabrizio Antenucci, Andrea Pagnani, Luca Leuzzi
• Format: Article
• Language: English
• Published: SciPost 2018-07-01
• Series: SciPost Physics
• Online Access: https://scipost.org/SciPostPhys.5.1.002

We propose and test improvements to state-of-the-art techniques of Bayeasian 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 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 mimicing 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.