Adaptive banding covariance estimation for high‐dimensional multivariate longitudinal data
Bibliographic record
Abstract
Abstract Modelling the covariance matrix of multiple responses in longitudinal data plays a vital role. It is more challenging than its univariate counterpart due to the presence of correlations among multiple responses. Using the modified Cholesky block decomposition, we impose an adaptive block‐banded structure on the Cholesky factor and sparsity on the innovation variance matrices via a novel convex hierarchical penalty and lasso penalty, respectively. The resulting adaptive block‐banding regularized estimator is fully data‐driven and has more flexibility than regular banding estimators. We develop an efficient alternative convex optimization algorithm using the Alternating Direction Method of Multipliers (ADMM) algorithm. The resulting estimators converge optimally in the Frobenius norm. We establish row‐specific support recovery for the precision matrix. Simulations and real data analysis show that the proposed estimator is better able to reveal banding sparsity patterns in data.
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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".