Model-Preserving Sensitivity Analysis for Families of Gaussian Distributions
This addresses the need for robust statistical modeling in domains like medicine, where data quality affects inference, though it is incremental as it builds on existing sensitivity analysis techniques.
The authors tackled the problem of sensitivity analysis in Gaussian graphical models, where standard methods break the conditional independence structure, by developing an approach that preserves the original graph's validity and quantifying variations with different measures, demonstrating robustness comparable to standard methods in artificial and medical applications.
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical model to misspecification of some of its underlying probabilities. In the context of graphical models, investigations of robustness fall under the notion of sensitivity analyses. These analyses consist in varying some of the model's probabilities or parameters and then assessing how far apart the original and the varied distributions are. However, for Gaussian graphical models, such variations usually make the original graph an incoherent representation of the model's conditional independence structure. Here we develop an approach to sensitivity analysis which guarantees the original graph remains valid after any probability variation and we quantify the effect of such variations using different measures. To achieve this we take advantage of algebraic techniques to both concisely represent conditional independence and to provide a straightforward way of checking the validity of such relationships. Our methods are demonstrated to be robust and comparable to standard ones, which break the conditional independence structure of the model, using an artificial example and a medical real-world application.