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LIT-354: Algebraic Geometry and Statistical Learning Theory

2 min read

Properties4
StatusUnavailable — seeded 2026-09-29 from metadata and published descriptions, not read; no lawful full text could be reached, and it stays Unavailable until a copy is supplied. Its core results are now read in a lawful substitute by the same author, Watanabe's A Widely Applicable Bayesian Information Criterion (LIT-616; arXiv 1208.6338, JMLR 2013). That paper restates the book's standard representation theorem, the real log canonical threshold and the free-energy asymptotics F = nL_n(w0) + λ log n − (m − 1) log log n, citing the book for each. Read it for the results; the book holds their proofs, the generalization-error theory and WAIC.
Version4
Tagslearning-theory, mathematics, probabilistic-modeling, model-comparison, information-geometry, anthology-candidate
Extended byLIT-616 — A Widely Applicable Bayesian Information Criterion

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Sumio Watanabe (2009), Cambridge University Press (Cambridge Monographs on Applied and Computational Mathematics 25) — DOI-10.1017/CBO9780511800474

Standing in the record

Registered on 2026-09-29 at the owner’s request, because the owner’s prior-art novelty map (a private working document on concepts as projectors, the linear representation hypothesis and their neighbours) cites it: row 15 must-cite: SLT owns degeneracy = singular Fisher; concept resolvability framed on it. It is seeded from metadata and published descriptions and has not been read here.

Identification notes: Not held in either record; anthology holds SLT follow-ons (ANTH-LIT-541 Murfet et al. “Deep Learning is Singular”, ANTH-LIT-542 local learning coefficient).

A close reading was attempted on 2026-09-29. No legitimate full text could be reached: The book is in copyright (Cambridge University Press 2009, Cambridge Monographs on Applied and Computational Mathematics 25; DOI 10.1017/CBO9780511800474, paywalled on Cambridge Core). OpenAlex marks it closed with no repository copy. Semantic Scholar resolves only the “Contents” front matter, with no open PDF. An Internet Archive advanced search by title returned no item. The converted-text cache holds no copy. I did not search the author’s own pages for a posted manuscript, and I know of no authorised full-text posting. It stays Deferred until a copy is supplied, not on merit.

Substitute (2026-10-03). The record reads the book’s core results in Watanabe’s A Widely Applicable Bayesian Information Criterion (LIT-616). It defines a model as regular when the map from parameters to distributions is one-to-one and the Fisher information is positive definite, and singular otherwise, which is the owner’s “degeneracy = singular Fisher”. It states the standard representation theorem (the book’s Theorem 6.1), the real log canonical threshold and its multiplicity, and the Bayes free-energy asymptotics, and cites the book for their proofs. The book would add those proofs, the theory of the generalization error, and WAIC.

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