Approximating Markov Processes by Averaging
Bibliographic record
Abstract
Normally, one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition. We, however, take a dual view of Markov processes as transformers of bounded measurable functions. This is very much in the same spirit as a “predicate-transformer” view, which is dual to the state-transformer view of transition systems. We redevelop the theory of labelled Markov processes from this viewpoint; in particular, we explore approximation theory. We obtain three main results. (i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximations. (iii) We show that there is a minimal process bisimulation-equivalent to a given process, and this minimal process is obtained as the limit of the finite approximants.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".