Sumio Watanabe's Algebraic Geometry and Statistical Learning Theory PDF

By Sumio Watanabe

certain to be influential, this e-book lays the principles for using algebraic geometry in statistical studying idea. Many commonplace statistical versions and studying machines utilized to info technological know-how have a parameter house that's singular: blend types, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity concept give you the valuable instruments for learning such non-smooth types. 4 major formulation are tested: 1. the log chance functionality could be given a standard typical shape utilizing answer of singularities, even utilized to extra complicated types; 2. the asymptotic behaviour of the marginal probability or 'the facts' is derived in response to zeta functionality concept; three. new tools are derived to estimate the generalization error in Bayes and Gibbs estimations from education mistakes; four. the generalization error of utmost probability and a posteriori equipment are clarified by means of empirical technique 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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