Semi-proximal augmented Lagrangian method for sparse estimation of high-dimensional inverse covariance matrices
Bibliographic record
Abstract
Estimating a large and sparse inverse covariance matrix is a fundamental problem in modern multivariate analysis.Recently, a generalized model for a sparse estimation was proposed in which an explicit eigenvalue bounded constraint is involved.It covers a large number of existing estimation approaches as special cases.It was shown that the dual of the generalized model contains five separable blocks, which cause more challenges for minimizing.In this paper, we use an augmented Lagrangian method to solve the dual problem, but we minimize the augmented Lagrangian function with respect to each variable in a Jacobian manner, and add a proximal point term to make each subproblem easy to solve.We show that this iterative scheme is equivalent to adding a proximal point term to the augmented Lagrangian function, and its convergence can be directly followed.Finally, we give numerical simulations by using the synthetic data which show that the proposed algorithm is very effective in estimating high-dimensional sparse inverse covariance matrices.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".