Algebraic geometry and statistical learning theory by Sumio Watanabe
Algebraic geometry and statistical learning theory Sumio Watanabe ebook
ISBN: 0521864674, 9780521864671
More specifically, the author uses the resolution of singularities theorem from real algebraic geometry to study statistical learning theory when the parameter space is highly singular. An Elementary Introduction to Statistical Learning Theory is an excellent book for courses on statistical learning theory, pattern recognition, and machine learning at the upper-undergraduat. Lugosi, (2004), Introduction to statistical learning theory. What assumptions are we as humans making that differ from those in learning theory? Information Geometry: Methods of Information Geometry Shun-Ichi Amari, Hiroshi Nagaoka Algebraic Geometry and Statistical Learning Theory Watanabe, Sumio Differential Geometry and Statistics M.K. These assumptions are probably something stronger than distribution-independent (e.g. (RStan lets you use Stan from within R.) Geometry and Data: Manifold Learning and Singular Learning machine-learning algorithms. Positive to be influential, Watanabe's guide lays the foundations for the use of algebraic geometry in statistical mastering concept. Singular learning theory draws from techniques in algebraic geometry to generalize the Bayesian Information Criterion (BIC) to a much wider set of models. There's a (involved) book “Algebraic Geometry and Statistical Learning Theory” by Sumio Watanabe which beyond above also develops (not terribly practical at the moment) methods for graphical models from that viewpoint. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. A new open source, software package called Stan lets you fit Bayesian statistical models using HMC.
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