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

By Sumio Watanabe

bound to be influential, this ebook lays the rules for using algebraic geometry in statistical studying idea. Many widespread statistical types and studying machines utilized to info technological know-how have a parameter house that's singular: combination types, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity idea give you the important instruments for learning such non-smooth versions. 4 major formulation are demonstrated: 1. the log chance functionality may be given a standard ordinary shape utilizing answer of singularities, even utilized to extra complicated versions; 2. the asymptotic behaviour of the marginal chance or 'the facts' is derived according to zeta functionality thought; three. new equipment are derived to estimate the generalization error in Bayes and Gibbs estimations from education error; four. the generalization mistakes of extreme chance and a posteriori tools are clarified through empirical strategy conception 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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