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This book establishes a rigorous mathematical foundation for applying algebraic geometry and singularity theory to statistical learning, particularly for models whose parameter spaces are singular (e.g., mixture models, neural networks, hidden Markov models, Bayesian networks, stochastic grammars). It shows how resolution of singularities and zeta‑function techniques can be used to standardize the likelihood function, derive asymptotic behavior of marginal likelihood (“evidence”), and estimate generalization errors of Bayesian and maximum‑likelihood estimators — thereby extending classical statistical theory to a broad class of realistic, non‑regular learning machines.

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245: $a: Algebraic Geometry and Statistical Learning Theory
245: $b:
082: $a:
100: $a: SUMIO WATANABE
650: $a: Mathematics
250: $a:
440: $v:
250: $b: Cambridge University Press
250: $c: 2009
020: $a: 978‑0521864671
300: $a: 300