Scalable Information Inequalities for Uncertainty Quantification

TL;DR

This paper introduces scalable information bounds for high-dimensional probabilistic models, enabling uncertainty quantification in large systems, long time regimes, and under model perturbations, with applications to statistical mechanics.

Contribution

It presents the first scalable information inequalities applicable to high-dimensional models, facilitating uncertainty bounds in complex, large-scale systems.

Findings

Derived robust uncertainty bounds for phase diagrams in statistical mechanics.

Enabled uncertainty quantification in large degrees of freedom and long time regimes.

Assessed impact of large model perturbations in nonlinear response regimes.

Abstract

In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for quantities of interest in the large degree of freedom limit and/or at long time regimes; (b) assess the impact of large model perturbations as in nonlinear response regimes in statistical mechanics; (c) address model-form uncertainty, i.e. compare different extended models and corresponding quantities of interest. We demonstrate some of these properties by deriving robust uncertainty quantification bounds for phase diagrams in statistical mechanics models.