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This content will become publicly available on December 21, 2024

Title: Causalized convergent cross-mapping and its approximate equivalence with directed information in causality analysis
Abstract

Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis—the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.

 
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Award ID(s):
2032709
NSF-PAR ID:
10522385
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
Editor(s):
Abbott, Derek
Publisher / Repository:
The National Academy of Sciences of the United States of America
Date Published:
Journal Name:
PNAS Nexus
Volume:
3
Issue:
1
ISSN:
2752-6542
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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