Sheaves as a Framework for Understanding and Interpreting Model Fit
This provides a general framework for researchers and practitioners dealing with structured data in complex systems, though it appears incremental as it adapts existing mathematical concepts to model analysis.
The paper tackles the problem of interpreting model fit in complex data systems by proposing sheaves as a framework to analyze local versus global fit, with applications ranging from sensor networks to deep learning feature spaces.
As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn from peripheral sources. In this paper we argue that in such situations, sheaves can provide a natural framework to analyze how well a statistical model fits at the local level (that is, on subsets of related datapoints) vs the global level (on all the data). The sheaf-based approach that we propose is suitably general enough to be useful in a range of applications, from analyzing sensor networks to understanding the feature space of a deep learning model.