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arXiv · 1708.00787

Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables

Alessia Marruzzo·Payal Tyagi·Fabrizio Antenucci·Andrea Pagnani·Luca Leuzzi
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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.

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Alessia Marruzzo, Payal Tyagi, Fabrizio Antenucci, Andrea Pagnani, Luca Leuzzi. 2017-08-02. Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables. https://doi.org/10.21468/scipostphys.5.1.002

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