Asymptotic Minimax Bounds for Stochastic Deconvolution Over Groups
Bibliographic record
Abstract
This paper examines stochastic deconvolution over noncommutative compact Lie groups. This involves Fourier analysis on compact Lie groups as well as convolution products over such groups. An observation process consisting of a known impulse response function convolved with an unknown signal with additive white noise is assumed. Data collected through the observation process then allow us to construct an estimator of the signal. Signal recovery is then assessed through integrated mean squared error for which the main results show that asymptotic minimaxity depends on smoothness properties of the impulse response function. Thus, if the Fourier transform of the impulse response function is bounded polynomially, then the asymptotic minimax signal recovery is polynomial, while if the Fourier transform of the impulse response function is exponentially bounded, then the asymptotic minimax signal recovery is logarithmic. Such investigations have been previously considered in both the engineering and statistics literature with applications in among others, medical imaging, robotics, and polymer science.
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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 | 0.007 | 0.027 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| 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".