Sheaves as a Framework for Understanding and Interpreting Model Fit

TL;DR

This paper proposes using sheaves as a versatile framework to analyze and interpret model fit at both local and global levels in complex, structured data systems, enhancing understanding across various applications.

Contribution

It introduces a sheaf-based approach for assessing model fit, bridging local and global analysis in complex data environments.

Findings

Sheaves effectively capture local-global fit discrepancies.

The framework applies to sensor networks and deep learning feature spaces.

Sheaves provide a unifying structure for interpretability in complex models.

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.