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Learning Driver-Response Relationships from Synchronization Patterns
chao-dyn · Submitted 6 Jul 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Instead, estimated interdependencies and mutual cross predictabilities depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect.
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The abstract, sentence by sentence
We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results as cross predictabilities used by previous authors. The systems which we study are asymmetrically coupled simple models (Lorenz, Roessler, and Henon models), the couplings being such as to lead to generalized synchronization. If the data were perfect (noisefree, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. This might no longer be true if the time series has finite length. Instead, estimated interdependencies and mutual cross predictabilities depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. We also show that slightly different variants of the interdependence measure can have quite different sensitivities.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. | contribution 0.77 | 0.81 | 0.04 | unclear 0.45 |
| s1 | We apply two recently proposed interdependence measures which should give similar results as cross predictabilities used by previous authors. | method 0.90 | 0.83 | 0.03 | hedged possibility 0.48 |
| s2 | The systems which we study are asymmetrically coupled simple models (Lorenz, Roessler, and Henon models), the couplings being such as to lead to generalized synchronization. | method 0.98 | 0.73 | 0.03 | asserted 0.97 |
| s3 | If the data were perfect (noisefree, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. | background 0.80 | 0.13 | 0.06 | hedged possibility 0.86 |
| s4 | This might no longer be true if the time series has finite length. | gap 0.48 | 0.09 | 0.07 | speculative 0.94 |
| s5 | Instead, estimated interdependencies and mutual cross predictabilities depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. | result 0.95 | 0.83 | 0.81 | asserted 0.99 |
| s6 | We also show that slightly different variants of the interdependence measure can have quite different sensitivities. | result 0.98 | 0.92 | 0.07 | asserted 1.00 |
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Original abstract
We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results as cross predictabilities used by previous authors. The systems which we study are asymmetrically coupled simple models (Lorenz, Roessler, and Henon models), the couplings being such as to lead to generalized synchronization. If the data were perfect (noisefree, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. This might no longer be true if the time series has finite length. Instead, estimated interdependencies and mutual cross predictabilities depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. We also show that slightly different variants of the interdependence measure can have quite different sensitivities.
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