Improved pseudolikelihood regularization and decimation methods on non-linearly interacting systems with continuous variables
Alessia Marruzzo, Payal Tyagi, Fabrizio Antenucci, Andrea Pagnani, Luca Leuzzi
SciPost Phys. 5, 002 (2018) · published 17 July 2018
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.
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- 1 2 Alessia Marruzzo,
- 2 Payal Tyagi,
- 2 3 Fabrizio Antenucci,
- 4 5 Andrea Pagnani,
- 2 6 Luca Leuzzi
- 1 CINECA [CINECA]
- 2 Istituto di Nanotecnologia [CNR-NANOTEC]
- 3 Université Paris-Saclay / University of Paris-Saclay
- 4 Human Genetics Foundation [HuGeF]
- 5 Italian Institute for Genomic Medicine [IIGM]
- 6 Sapienza – Università di Roma / Sapienza University of Rome
- European Research Council [ERC]
- Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])