Get Algebraic Geometry and Statistical Learning Theory PDF

By Sumio Watanabe

bound to be influential, this ebook lays the principles for using algebraic geometry in statistical studying conception. Many everyday statistical versions and studying machines utilized to details technology have a parameter area that's singular: mix versions, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are significant examples. Algebraic geometry and singularity concept give you the beneficial instruments for learning such non-smooth versions. 4 major formulation are proven: 1. the log probability functionality could be given a typical normal shape utilizing answer of singularities, even utilized to extra advanced types; 2. the asymptotic behaviour of the marginal chance or 'the facts' is derived in keeping with zeta functionality conception; three. new tools are derived to estimate the generalization error in Bayes and Gibbs estimations from education blunders; four. the generalization blunders of utmost probability and a posteriori equipment are clarified via empirical method concept 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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