Bibliographic record
Abstract
In this paper, we carry out a unified study for L_1 over L_2 sparsity promoting models, which are widely used in the regime of coherent dictionaries for recovering sparse nonnegative/arbitrary signal. First, we provide the exact recovery condition on both the constrained and the unconstrained models for a broad set of signals. Next, we prove the solution existence of these L_{1}/L_{2} models under the assumption that the null space of the measurement matrix satisfies the $s$-spherical section property. Then by deriving an analytical solution for the proximal operator of the L_{1} / L_{2} with nonnegative constraint, we develop a new alternating direction method of multipliers based method (ADMM$_p^+$) to solve the unconstrained model. We establish its global convergence to a d-stationary solution (sharpest stationary) and its local linear convergence under certain conditions. Numerical simulations on two specific applications confirm the superior of ADMM$_p^+$ over the state-of-the-art methods in sparse recovery. ADMM$_p^+$ reduces computational time by about $95\%\sim99\%$ while achieving a much higher accuracy compared to commonly used scaled gradient projection method for wavelength misalignment problem.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".