Path Space Cochains and Population Time Series Analysis
Chad Giusti, Darrick Lee · arXiv (Cornell University) · 2018
One of the core advantages topological methods for data analysis provide is that the language of (co)chains can be mapped onto the semantics of the data, providing a natural avenue for human understanding of the results. Here, we describe such a semantic structure on Chen's classical iterated integral cochain model for paths in Euclidean space. Specifically, in the context of population time series data, we observe that iterated integrals provide a model-free measure of pairwise influence that can be used for causality inference. Along the way, we survey the construction of the iterated integral model, including recent results and applications, and briefly survey the current standard methods for causality inference.