Optimal scaling of Metropolis algorithms: is 0.234 as robust as believed. Universite de Montreal and University of Toronto, email: bedard@dms.umontreal.ca
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Bibliographic record
Abstract
Abstract The Metropolis algorithm with Gaussian proposal distribution is a popular samplingmethod; it is versatile and easy to implement. Optimal scaling theory aims to improve the speed of convergence of this algorithm to its stationary distribution by carefullyselecting its tuning parameter. This paper is an overview of existing optimal scaling results and addresses in more depth the case of high-dimensional target distributionsformed of independent, but not identically distributed components. It attempts to give an intuitive explanation as to when the previously-derived optimal acceptance rate of0.234 is indeed optimal, and when it is unsuitable. In the latter case, it also explains how to find the correct asymptotically optimal acceptance rate, and why we sometimes haveto turn to inhomogeneous proposal variances in order to obtain an efficient algorithm. This is all illustrated with a simple example.
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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 | 0.000 | 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 it