Multi-level Monte Carlo for continuous time Markov chains, with\n applications in biochemical kinetics
Bibliographic record
Abstract
We show how to extend a recently proposed multi-level Monte Carlo approach to\nthe continuous time Markov chain setting, thereby greatly lowering the\ncomputational complexity needed to compute expected values of functions of the\nstate of the system to a specified accuracy. The extension is non-trivial,\nexploiting a coupling of the requisite processes that is easy to simulate while\nproviding a small variance for the estimator. Further, and in a stark departure\nfrom other implementations of multi-level Monte Carlo, we show how to produce\nan unbiased estimator that is significantly less computationally expensive than\nthe usual unbiased estimator arising from exact algorithms in conjunction with\ncrude Monte Carlo. We thereby dramatically improve, in a quantifiable manner,\nthe basic computational complexity of current approaches that have many names\nand variants across the scientific literature, including the\nBortz-Kalos-Lebowitz algorithm, discrete event simulation, dynamic Monte Carlo,\nkinetic Monte Carlo, the n-fold way, the next reaction method,the\nresidence-time algorithm, the stochastic simulation algorithm, Gillespie's\nalgorithm, and tau-leaping. The new algorithm applies generically, but we also\ngive an example where the coupling idea alone, even without a multi-level\ndiscretization, can be used to improve efficiency by exploiting system\nstructure. Stochastically modeled chemical reaction networks provide a very\nimportant application for this work. Hence, we use this context for our\nnotation, terminology, natural scalings, and computational examples.\n
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".