Negative ridge regression parameters for improving the covariance structure of multivariate linear downscaling models
Bibliographic record
Abstract
Abstract A downscaling model for multivariate data, e.g. weather elements recorded at multiple sites, should not only be able to fit each of the observed series well, but it should also be able to reproduce observed relationships between the variables. In a linear sense, this means accurately simulating the observed covariance matrix. Multivariate ridge regression with negative ridge parameters is introduced as a means of accomplishing this goal. The procedure is conceptually similar to expanded downscaling: both force the covariance structure of the predictions to match that of observations. Unlike expanded downscaling, an explicit constraint on the covariance matrix is not added to the regression cost function. Instead, regression coefficients are estimated directly via a matrix equation, while ridge parameters, which are free to take positive or negative values, are adjusted iteratively such that the discrepancy between modelled and observed covariance matrices is minimized. Results from multi‐site temperature and precipitation data suggest that the proposed method is capable of constraining the predicted covariance matrix to closely match the observed. © Crown in the right of Canada. Published by John Wiley & Sons, Ltd
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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 | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".