000			01894 a2200229 4500
008			240502b |||||||| |||| 00| 0 eng d
020			_a9780521864671
082			_a006.31 WAT
100			_aWatanabe, Sumio
245			_aAlgebraic geometry and statistical learning theory
260			_aCambridge: _bCambridge University Press, _c2009
300			_aviii, 286p.: _bhbk.: _c23cm
440			_aCambridge Monographs on Applied and Computational Mathematics, 25
520			_aSure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory on algebraic varieties. https://www.cambridge.org/in/universitypress/subjects/computer-science/pattern-recognition-and-machine-learning/algebraic-geometry-and-statistical-learning-theory?format=HB
650			_aAlgebraic Geometry
650			_aAlgebra
650			_aComputational Learning Theory
650			_aMathematics
650			_aComputational Science
650			_aComputer Science
942			_cTD _2ddc
999			_c60403 _d60403