Local probability distribution of natural signals in sparse domains
Bibliographic record
Abstract
In this paper we investigate the local probability density function (pdf) of natural signals in sparse domains. The statistical properties of natural signals are characterized more accurately in the sparse domains because the sparse domain coefficients (SDCs) have heavy-tailed distribution and have reduced correlation with adjacent coefficients. Our experiments show that a conditionally (given locally estimated variance and shape) independent Bessel K-form (BKF) pdf locally fits the sparse domain's coefficients of natural signals, accurately. To justify this observation, we also investigate the pdf of the locally estimated variance and suggest a Gamma pdf for the locally estimated variance. Since commonly used sparse transformations are orthonormal, the pdf of the sparse domain coefficients must converge to Gaussian distribution by virtue of central limit theorem assuming that natural signals are locally wide sense stationary for small window sizes. Interestingly, we observe that the pdf of the normalized data (on the locally estimated variance) exhibit a Gaussian pdf, which justifies why the BKF pdf is an appropriate fit.
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How this classification was reachedexpand
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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".