A new information-theoretic approach to signal denoising and best basis selection
Bibliographic record
Abstract
The problem of signal denoising with an orthogonal basis is considered. The existing approaches convert the considered problem into one of finding a threshold for estimates of basis coefficients. In this paper, a new solution to the denoising problem is proposed. The method is based on the description length of the noiseless data in subspaces of the bases. For each subspace, we estimate the desired description length and suggest choosing the subspace for which this quantity is minimized. We provide a method of probabilistically estimating the reconstruction error. This estimate is used for probabilistic validation of the desired description length. In existing thresholding methods, the optimum threshold is obtained as a function of the additive noise variance. In practical problems, where the noise variance is unknown, the first step is to estimate the noise variance. The estimated noise variance is then used in calculating the optimum threshold. Unlike such approaches, in the proposed method, the noise variance estimation and the signal denoising are done simultaneously.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".