Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function
Bibliographic record
Abstract
In this work, a novel learning‐based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state‐of‐the‐art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter‐column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real‐world data confirm the superiority of the proposed approach to the less recent methods.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.001 |
| 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".