Model Uncertainty and Correctability for Directed Graphical Models

TL;DR

This paper introduces information-theoretic methods to quantify, rank, and correct sources of uncertainty in directed graphical models, enhancing their reliability in scientific applications.

Contribution

It develops robust uncertainty quantification and correction techniques for directed graphical models, enabling systematic improvement of model components based on their impact.

Findings

Effective uncertainty ranking of model sources

Successful correction of impactful model components

Improved accuracy in chemical kinetics and materials screening

Abstract

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.