Theoretical and Empirical Results for Recovery From Multiple Measurements
Bibliographic record
Abstract
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely studied in compressed sensing. We study the recovery properties of two algorithms for problems with noiseless data and exact-sparse representation. First, we show that recovery using sum-of-norm minimization cannot exceed the uniform-recovery rate of sequential SMV usingl1minimization, and that there are problems that can be solved with one approach, but not the other. Second, we study the performance of the ReMBo algorithm (M. Mishali and Y. Eldar, ¿Reduce and boost: Recovering arbitrary sets of jointly sparse vectors,¿IEEE Trans. Signal Process., vol. 56, no. 10, 4692-4702, Oct. 2008) in combination withl1minimization, and show how recovery improves as more measurements are taken. From this analysis, it follows that having more measurements than the number of linearly independent nonzero rows does not improve the potential theoretical recovery rate.
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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 | 0.022 | 0.158 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.007 | 0.010 |
| Science and technology studies | 0.003 | 0.009 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.006 | 0.007 |
| Research integrity | 0.005 | 0.009 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".