Improved estimation in tensor regression with multiple change-points
Bibliographic record
Abstract
In this paper, we consider an estimation problem about the tensor coefficient in a tensor regression model with multiple and unknown change-points. We generalize some recent findings in five ways. First, the problem studied is more general than the one in context of a matrix parameter with multiple change-points. Second, we develop asymptotic results of the tensor estimators in the context of a tensor regression with unknown change-points. Third, we construct a class of shrinkage tensor estimators that encompasses the unrestricted estimator (UE) and the restricted estimator (RE). Fourth, we generalize some identities which are crucial in deriving the asymptotic distributional risk (ADR) of the tensor estimators. Fifth, we show that the proposed shrinkage estimators perform better than the UE. The additional novelty of the established results consists in the fact that the dependence structure of the errors is as weak as that of an L2-mixingale. Finally, the theoretical results are corroborated by the simulation findings and our methods are applied to analyse MRI and fMRI datasets.
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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 | 0.012 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".