The Generalized Ridge Trace Plot: Visualizing Bias<i>and</i>Precision
Bibliographic record
Abstract
In ridge regression and related shrinkage methods, the ridge trace plot, a plot of estimated coefficients against a shrinkage parameter, is a common graphical adjunct to help determine a favorable trade-off of bias against precision (inverse variance) of the estimates. However, standard unidimensional versions of this plot are ill-suited for this purpose because they show only bias directly and ignore the multidimensional nature of the problem.A generalized version of the ridge trace plot is introduced, showing covariance ellipsoids in parameter space, whose centers show bias and whose size and shape show variance and covariance, respectively, in relation to the criteria for which these methods were developed. These provide a direct visualization of both bias and precision. Even two-dimensional bivariate versions of this plot show interesting features not revealed in the standard univariate version. Low-rank versions of this plot, based on an orthogonal transformation of predictor space extend these ideas to larger numbers of predictor variables, by focusing on the dimensions in the space of predictors that are likely to be most informative about the nature of bias and precision. Two well-known datasets are used to illustrate these graphical methods. The genridge package for R implements computation and display.
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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 | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".