Bibliographic record
Abstract
This article introduces a technique for estimating samples of a random signal based on observations made by several observers and at different sampling rates. We consider a discrete-time mathematical model where an observer sees the original random signal x(n) through a bank of sensors which we model by linear filters and downsamplers. Each sensor, therefore, outputs a measurement signal v/sub i/(n) whose sampling rate is only a fraction of the sampling rate assumed for the original signal under observation. It is straightforward to show that the optimal least-mean-squares estimator for our problem is a linear operator F operating on v/sub i/(n)s. We observe, however, that to find F we need to know the power spectral density P/sub x/(e/sup jw/) of x(n) which is itself not observable. This motivates us to consider the possibility of estimating P/sub x/(e/sup jw/) using the observable low-rate data. We show that the statistical inference problem which addresses estimation of P/sub x/(e/sup jw/) given certain statistics of v/sub i/(n) is mathematically ill-posed. We resolve this ill-posed inference problem using the principle of maximum entropy. We show, moreover, that the proposed maximum entropy inference technique is a continuous mapping. Therefore, one might safely use it to estimate P/sub x/(e/sup jw/) based on approximate statistics of v/sub i/(n) obtained from the samples.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".