The Canonical Bicoherence—Part I: Definition, Multitaper Estimation, and Statistics
Bibliographic record
Abstract
The central theme of this pair of papers (Parts I and II) [IEEE Transactions on Signal Processing, vol. 57, no. 4, April 2009] is a new definition: the canonical bicoherence, a combination of the canonical coherence and the bicoherence. The canonical bicoherence is an effective tool for analyzing quadratic nonlinearity in multivariate signals. In this first part, the definition and properties of the canonical bicoherence are presented. The feasibility of the canonical bicoherence in detecting quadratic phase coupling (QPC) of multivariate signals is explained theoretically, illustrated by an example, and verified by numerical simulations. Multitaper methods and a sequence of three singular value decompositions (SVD's) are used to estimate canonical bicoherences, to achieve reliable estimates with a reasonable amount of memory and computation time. Finally, we show that the canonical bicoherence estimate has an approximate asymptotic kappachi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nu</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -distribution, and the weighted jackknife method, used over tapers and segments, is applied to estimate variances of multitaper canonical bicoherence estimates.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".