Sheaves as a Framework for Understanding and Interpreting Model Fit

• URL: http://arxiv.org/abs/2105.10414v1
• Date: Fri, 21 May 2021 15:34:09 GMT
• Title: Sheaves as a Framework for Understanding and Interpreting Model Fit
• Authors: Henry Kvinge, Brett Jefferson, Cliff Joslyn, Emilie Purvine
• Abstract summary: We argue that sheaves can provide a natural framework to analyze how well a statistical model fits at the local level. The sheaf-based approach is suitably general enough to be useful in a range of applications.
• Score: 2.867517731896504
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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