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As data grows in size and complexity, finding frameworks which aid ininterpretation and analysis has become critical. This is particularly true whendata comes from complex systems where extensive structure is available, butmust be drawn from peripheral sources. In this paper we argue that in suchsituations, sheaves can provide a natural framework to analyze how well astatistical model fits at the local level (that is, on subsets of relateddatapoints) vs the global level (on all the data). The sheaf-based approachthat we propose is suitably general enough to be useful in a range ofapplications, from analyzing sensor networks to understanding the feature spaceof a deep learning model.

Sheaves as a Framework for Understanding and Interpreting Model Fit