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

TL;DR

This paper introduces improved Bayesian inference techniques using pseudolikelihood regularization and decimation for non-linear continuous systems, demonstrating their effectiveness in identifying correct models despite noise and incorrect hypotheses.

Contribution

It presents novel methods for optimal regularization parameter selection and decimation stopping criteria, enhancing inference accuracy in complex non-linear systems.

Findings

Methods effectively distinguish correct from wrong hypotheses as data size increases.

Techniques perform well with noisy, non-linear data.

Decimation criteria are robust even without sharp peaks in pseudolikelihood.

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.