Download e-book for iPad: 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 thought. Many generic statistical versions and studying machines utilized to details technological know-how have a parameter area that's singular: combination versions, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity idea give you the priceless instruments for learning such non-smooth types. 4 major formulation are confirmed: 1. the log probability functionality might be given a typical general shape utilizing solution of singularities, even utilized to extra advanced types; 2. the asymptotic behaviour of the marginal probability or 'the facts' is derived in response to zeta functionality thought; three. new tools are derived to estimate the generalization blunders in Bayes and Gibbs estimations from education error; four. the generalization error of extreme chance and a posteriori equipment are clarified by means of empirical method 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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