Model Uncertainty and Correctability for Directed Graphical Models
This addresses model uncertainty and correctability for researchers using directed graphical models in fields like machine learning and physico-chemical applications, offering a mathematically rigorous approach to systematic improvement.
The paper tackles the problem of multi-sourced model uncertainty in directed graphical models by developing information-theoretic methods and stress tests to quantify and propagate uncertainties to quantities of interest, enabling ranking and correction of impactful components while controlling new errors, as demonstrated in physico-chemical examples like quantum scale-informed chemical kinetics and materials screening for fuel cells.
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.