Java Code to Explain Probabilistic Bisimilarity Distances for Labelled Markov Chains
Bibliographic record
Abstract
Probabilistic bisimilarity distances [3] measure the similarity of behaviour of states of a labelled Markov chain. The smaller the distance between two states, the more alike they behave. Their distance is zero if and only if they are probabilistic bisimilar. Recently, algorithms have been developed that can compute probabilistic bisimilarity distances for labelled Markov chains with thousands of states within seconds. However, say we compute that the distance of two states is 0.125. How does one explain that 0.125 captures the similarity of their behaviour? In [2], we address this question by returning to the definition of probabilistic bisimilarity distances proposed by Desharnais, Gupta, Jagadeesan, and Panangaden [1] more than two decades ago. We use a slight variation of their logic to construct for each pair of states a sequence of formulas that explains the probabilistic bisimilarity distance of the states. Furthermore, we present an algorithm that computes those formulas and we show that each formula can be computed in polynomial time. Here, we provide an implementation of that algorithm in Java. [1] Josée Desharnais, Vineet Gupta, Radha Jagadeesan, and Prakash Panangaden. Metrics for labeled Markov systems. In Jos Baeten and Sjouke Mauw, editors, Proceedings of the 10th International Conference on Concurrency Theory, volume 1664 of Lecture Notes in Computer Science, pages 258-273, Eindhoven, The Netherlands, August 1999. Springer-Verlag. [2] Amgad Rady and Franck van Breugel. Explainability of probabilistic bisimilarity distances for labelled Markov chains. In Pawel Sobocinski and Orna Kupferman, editors, Proceedings of the 26th International Conference on Foundations of Software Science and Computational Structures, Paris, France, April 2023. [3] Franck van Breugel. Probabilistic bisimilarity distances. ACM SIGLOG News, 4(4), 33-51, October 2017.
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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 | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.039 | 0.013 |
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".