Bayesian Partial Reduced-Rank Regression
Bibliographic record
Abstract
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously.However, RR regression models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix.To address this limitation, a Bayesian Partial RR (BPRR) regression is exploited, where the response vector and the coefficient matrix are partitioned into low-and full-rank sub-groups.As opposed to the literature, which assumes known group structure and rank, a novel strategy is introduced that treats them as unknown parameters to be estimated.The main contribution is 2-fold: an approach to infer the low-and full-rank group memberships from the data is proposed, and then, conditionally on this allocation, the corresponding (reduced) rank is estimated.Both steps are carried out in a Bayesian approach, allowing for full uncertainty quantification and based on a partially collapsed Gibbs sampler.It relies on a Laplace approximation of the marginal likelihood and the Metropolized Shotgun Stochastic Search to estimate the group allocation efficiently.Applications to synthetic and real-world data reveal the potential of the proposed method to reveal hidden structures in the data.
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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 | 0.007 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".