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

By Sumio Watanabe

ISBN-10: 0521864674

ISBN-13: 9780521864671

guaranteed to be influential, this ebook lays the rules for using algebraic geometry in statistical studying concept. Many widespread statistical versions and studying machines utilized to info technology have a parameter area that's singular: combination types, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity thought give you the worthy instruments for learning such non-smooth versions. 4 major formulation are verified: 1. the log probability functionality should be given a standard normal shape utilizing answer of singularities, even utilized to extra complicated versions; 2. the asymptotic behaviour of the marginal chance or 'the proof' is derived according to zeta functionality conception; three. new equipment are derived to estimate the generalization mistakes in Bayes and Gibbs estimations from education blunders; four. the generalization error of utmost probability and a posteriori tools are clarified by means of empirical approach 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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