Аннотация:
Statistical and mechanistic models are crucial in studying dynamic neurobiological processes. Often these models can be translated into (possibly directed) graphs, and being able to efficiently perform statistical learning on sets of these graphs may be of crucial interest to clinicians and researchers alike. While network science approaches have been immensely useful in this regard, we expect that novel methodologies will provide answers to inference and prediction problems beyond those that have been introduced in the literature. To this end, we develop a framework that associates generalized metric space structures to graphs, and further embeds these structures in a global pseudometric space equipped with rich theoretical and practical properties. As an application, we show how to incorporate path homology–an algebro-topological descriptor of directed graphs–into a persistence framework that inherits stability and convergence properties from this pseudometric. We conclude by describing how this pseudometric further admits geometry-aware, practically-computable relaxations via the theory of optimal transport.
Язык доклада: английский
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