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

Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca

doi:10.21468/SciPostPhys.5.1.002

SciPost Physics

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

doi: 10.21468/SciPostPhys.5.1.002
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.5.1.002
TI  - Improved pseudolikelihood regularization and decimation methods on non-linearly interacting systems with continuous variables
PY  - 2018/07/17
UR  - https://scipost.org/SciPostPhys.5.1.002
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 5
IS  - 1
SP  - 002
A1  - Marruzzo, Alessia
AU  - Tyagi, Payal
AU  - Antenucci, Fabrizio
AU  - Pagnani, Andrea
AU  - Leuzzi, Luca
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.5.1.002,
	title={{Improved pseudolikelihood regularization and decimation methods on non-linearly interacting systems with continuous variables}},
	author={Alessia Marruzzo and Payal Tyagi and Fabrizio Antenucci and Andrea Pagnani and Luca Leuzzi},
	journal={SciPost Phys.},
	volume={5},
	pages={002},
	year={2018},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.5.1.002},
	url={https://scipost.org/10.21468/SciPostPhys.5.1.002},
}

Cited by 5

Ontology / Topics

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Bayesian statistical inference Decimation

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¹ ² Alessia Marruzzo,
² Payal Tyagi,
² ³ Fabrizio Antenucci,
⁴ ⁵ Andrea Pagnani,
² ⁶ Luca Leuzzi

Funders for the research work leading to this publication

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])