Variance Reduction via Antithetic Markov Chains
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Bibliographic record
Abstract
We present a Monte Carlo integration method, antithetic Markov chain sampling (AMCS), that incorporates local Markov transitions in an un-derlying importance sampler. Like sequential Monte Carlo sampling, the proposed method uses a sequence of Markov transitions to guide the sampling toward influential regions of the in-tegrand (modes). However, AMCS differs in the type of transitions that may be used, the num-ber of Markov chains, and the method of chain termination. In particular, from each point sam-pled from an initial proposal, AMCS collects a sequence of points by simulating two indepen-dent, but antithetic Markov chains, which are terminated by a sample-dependent stopping rule. Such an approach provides greater flexibility for targeting influential areas while eliminating the need to fix the length of the Markov chain a pri-ori. We show that the resulting estimator is un-biased and can reduce variance on peaked multi-modal integrands that challenge current methods. 1
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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 | 0.001 |
| Open science | 0.001 | 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