Download e-book for kindle: Algebraic Geometry and Statistical Learning Theory by Sumio Watanabe

By Sumio Watanabe

absolute to be influential, this ebook lays the principles for using algebraic geometry in statistical studying concept. Many ordinary statistical versions and studying machines utilized to details technological know-how have a parameter house that's singular: mix types, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity idea give you the valuable instruments for learning such non-smooth types. 4 major formulation are tested: 1. the log probability functionality might be given a typical common shape utilizing answer of singularities, even utilized to extra advanced types; 2. the asymptotic behaviour of the marginal probability or 'the proof' is derived according to zeta functionality concept; three. new equipment are derived to estimate the generalization blunders in Bayes and Gibbs estimations from education blunders; four. the generalization mistakes of utmost probability and a posteriori tools are clarified by means of empirical method idea on algebraic varieties.

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Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics) by Sumio Watanabe

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