Information topology identifies emergent model classes

Understand

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived.

• Using Information Geometry, we consider geometric properties of statistical models for different observations.
• As observations are varied, the model manifold may be stretched, compressed, or even collapsed.
• Observations that preserve the structural identifiability of the parameters also preserve certain topological features (such as edges and corners) that characterize the model's underlying physical principles.