  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.
