Mysteries Department
Sign inRequest access
MethodsSimulation-based inferenceNeural posterior estimation for the period-cipher family, with simulation-based calibration
Method · simulation-based inference

Neural posterior estimation for the period-cipher family, with simulation-based calibration

Problem Track A can't solve: which settings of the period-cipher family the text actually pins down, with calibrated uncertainty. Rejection ABC (M-T39) gives a best-5 % set, which depends on a threshold and doesn't say which settings are identified. Track A takes its cipher setting from that fit.

Simulation-based inferenceVersion 1.0Licence MIT3 runsUsed on 1 mystery

Questions it answers

Code Python

Download module (.py)npe_t42.pyView source

Runs and results 3 runs

RunMysteryMeasuredResultAgainstDate
RUN0DCF8MBKZFHJVoynichSBC coverage of 90 % sets per setting; mean log posterior of the true setting (NPE vs ABC); posterior predictive misses on held-out pagesevery setting covered on 96-100 % of draws; mean log score NPE -0.784 vs ABC -0.968. Posterior modes: Herbal A stream spacing, 400-word nomenclator, 1 homophone per vowel and 4 per consonant kept 98 %, vowels dropped, simplified spelling, 5 % copied nulls, line layer 0.25; Herbal B stream, 400-word nomenclator, no homophones, no copied nulls, line layer 0.5. Pinned down (entropy under half the prior's): spacing, syllable signs, line layer, positional forms (and nomenclator size in B). Posterior predictive on held-out pages: 2/12 held-out statistics missed (A), 1/12 (B)T39 rejection ABC best settings: 5/12 (A), 3/12 (B) on held-out pages with one setting and 10 seeds
RUN0DCF9FZ5EPZSVoynichHeld-out statistics missed (|z| > 2, of 12) and of all 30, on held-out pages; one setting, seeds 5000-5009 (T39's confirmation exactly)Herbal A 3/12, 13/30 (training pages 6/12, 15/30); Herbal B 2/12, 6/30 (training 1/12, 4/30)T39 best settings, same scoring: Herbal A 5/12, 15/30 · Herbal B 3/12, 9/30
RUN0DCG56DG7RVQVoynichOut-of-fold 90 % coverage in the truncated region; held-out statistics missed by the new posterior mode (10 seeds, T39 scoring)coverage at least 0.954 for every setting in both sections. New modes: Herbal A as round 1 but no copied nulls (4/12 held-out, 14/30); Herbal B now no nomenclator, no homophones, 5 % copied nulls (3/12, 6/30). The 99.9 % region kept 46 of 47 setting values for A and 42 for BRound-1 modes (generation 2): A 3/12, 13/30 · B 2/12, 6/30. T39: A 5/12, 15/30 · B 3/12, 9/30

Applied to

Voynich Manuscript
3 datasetsHerbal A and Herbal B paragraph text: training and held-out pages, Latin genre texts, ZL3b transcription

References

  1. Cranmer, K., Brehmer, J., Louppe, G. 2020. The frontier of simulation-based inference. Proceedings of the National Academy of Sciences.
  2. Csilléry, K., François, O., Blum, M. 2011. abc: an R package for Approximate Bayesian Computation (ABC). arXiv.
  3. Talts, S., Betancourt, M., Simpson, D. et al. 2018. Validating Bayesian Inference Algorithms with Simulation-Based Calibration. arXiv.
  4. Advances in Neural Information Processing Systems 29 (NIPS 2016); arXiv:1605.06376 (both pages checked). Neural posterior estimation: a mixture density network trained on simulations replaces rejection ABC. Track B: fitting the period-cipher family (M-T39) without a rejection threshold, checked with simulation-based calibration [@talts2018validating].
Private beta Downloads are for beta members

We're in a private beta while we get things right. Everything here is free to read; downloading datasets, sources and code is open to members for now.

Apply to the betaSign in
It takes a couple of minutes. We'll reply by email.