A Distributed Computer System for Parallel Markov Chain Monte Carlo (MCMC)
Bibliographic record
Abstract
A ubiquitous problem in physics is to determine expectation values of observables associated with a system. This problem is typically formulated as an integration of some likelihood over a multidimensional parameter space. In Bayesian analysis, numerical Markov Chain Monte Carlo (MCMC) algorithms are employed to solve such integrals using a fixed number of samples in the Markov Chain. In general, MCMC algorithms are computationally expensive for large datasets and have difficulties sampling from multimodal parameter spaces. An MCMC implementation that is robust and inexpensive for researchers is desired. Distributed computing systems have shown the potential to act as virtual supercomputers, such as in the SETI@home project in which millions of private computers participate. We propose that a clustered peer-to-peer (P2P) computer network serves as an ideal structure to run Markovian state exchange algorithms such as Parallel Tempering (PT). PT overcomes the difficulty in sampling from multimodal distributions by running multiple chains in parallel with different target distributions andexchanging their states in a Markovian manner. To demonstrate the feasibility of peer-to-peer Parallel Tempering (P2P PT), a simple two-dimensional dataset consisting of two Gaussian signals separated by a region of low probability was used in a Bayesian parameter fitting algorithm. A small connected peer-to-peer network was constructed using separate processes on a linux kernel, and P2P PT was applied to the dataset. These sampling results were compared with those obtained from sampling the parameter space with a single chain. It was found that the single chain was unable to sample both modes effectively, while the P2P PT method explored the target distribution well, visiting both modes approximately equally. Future work will involve scaling to many dimensions and large networks, and convergence conditions with highly heterogeneous computing capabilities of members within the network.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.025 | 0.009 |
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".