Efficient LED‐SAC Sparse Estimator Using Fast Sequential Adaptive Coordinate‐Wise Optimization (LED‐2SAC)
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Bibliographic record
Abstract
Solving the underdetermined system of linear equations is of great interest in signal processing application, particularly when the underlying signal to be estimated is sparse. Recently, a new sparsity encouraging penalty function is introduced as Linearized Exponentially Decaying penalty, LED, which results in the sparsest solution for an underdetermined system of equations subject to the minimization of the least squares loss function. A sequential solution is available for LED‐based objective function, which is denoted by LED‐SAC algorithm. This solution, which aims to sequentially solve the LED‐based objective function, ignores the sparsity of the solution. In this paper, we present a new sparse solution. The new method benefits from the sparsity of the signal both in the optimization criterion (LED) and its solution path, denoted by Sparse SAC (2SAC). The new reconstruction method denoted by LED‐2SAC (LED‐Sparse SAC) is consequently more efficient and considerably fast compared to the LED‐SAC algorithm, in terms of adaptability and convergence rate. In addition, the computational complexity of both LED‐SAC and LED‐2SAC is shown to be of order 𝒪 ( d 2 ), which is better than the other batch solutions like LARS. LARS algorithm has complexity of order 𝒪 ( d 3 + n d 2 ), where d is the dimension of the sparse signal and n is the number of observations.
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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 it