Estimating time delays for constructing dynamical networks
Bibliographic record
Abstract
Abstract. Dynamical networks – networks inferred from multivariate time series – have been widely applied to climate data and beyond, resulting in new insights into the underlying dynamics. However, these inferred networks can suffer from biases that need to be accounted for to properly interpret the results. Here, we report on a previously unrecognized bias in the estimate of time delays between nodes in dynamical networks inferred from cross-correlations, a method often used. This bias results in the maximum correlation occurring disproportionately often at large time lags. This is of particular concern in dynamical networks where the large number of possible links necessitates finding the correct time lag in an automated way. We show that this bias can arise due to the similarity of the estimator to a random walk, and are able to map them to each other explicitly for some cases. For the random walk there is an analytical solution for the bias that is closely related to the famous Lévy arcsine distribution, which provides an upper bound in many other cases. Finally, we show that estimating the cross-correlation in frequency space effectively eliminates this bias. Reanalysing large lag links (from a climate network) with this method results in a distribution peaked near zero instead, as well as additional peaks at the originally assigned lag. Links that are reassigned smaller time lags tend to have a smaller distance between them, which indicates that the new time delays are physically reasonable.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".