Layered multishift coupling for use in perfect sampling algorithms (with a primer on CFTP)
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract. In this article we describe a new coupling technique which is useful in a variety of perfect sampling algorithms. A multishift coupler generates a random function f() so that for each x ∈ R, f(x) − x is governed by the same fixed probability distribution, such as a normal distribution. We develop the class of layered multishift couplers, which are simple and have several useful properties. For the standard normal distribution, for instance, the layered multishift coupler generates an f() which (surprisingly) maps an interval of length ℓ to fewer than 2+ℓ/2.35 points — useful in applications which perform computations on each such image point. The layered multishift coupler improves and simplifies algorithms for generating perfectly random samples from several distributions, including the autogamma distribution, posterior distributions for Bayesian inference, and the steady state distribution for certain storage systems. We also use the layered multishift coupler to develop a Markov-chain based perfect sampling algorithm for the autonormal distribution. At the request of the organizers, we begin by giving a primer on CFTP (coupling from the past); CFTP and Fill’s algorithm are the two predominant techniques for generating perfectly random samples using coupled Markov chains.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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