Source-linked AI summary
Measuring Information Transfer
Thomas Schreiber
TL;DR
Delayed mutual information cannot distinguish exchanged information from dependence due to shared history or input; transfer entropy uses transition probabilities to quantify directional dependence. In map systems it identifies one-way coupling, and in a sleep-apnea series it indicates stronger heart-to-breath than reverse flow.
Problem
Time-delayed mutual information does not explicitly separate exchanged information from dependence due to common input signals or history.
Source: p. 1Method
Transfer entropy quantifies how another system's state influences transition probabilities, with known common inputs conditionable out when computationally feasible.
Source: p. 2Results
Transfer entropy reflected one-way coupling in the map systems, including a zero reverse rate across Ulam coupling strengths, and indicated stronger heart-to-breath than reverse flow in one sleep-apnea series.
Source: pp. 3–4Takeaways & Limitations
It supports assessing directional information exchange separately from shared dependence, and known common input can be conditioned out when feasible.
Source: pp. 1–2
Abstract
from arXiv · showhide
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish driving and responding elements and to detect asymmetry in the coupling of subsystems.