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Algebraic geometry and statistical learning theory Sumio Watanabe
Publisher: CUP

Christian P.Robert, George Casella. 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. Monte Carlo Statistical Methods. Which means that some students enter my class having already studied Algebra. Singular learning theory draws from techniques in algebraic geometry to generalize the Bayesian Information Criterion (BIC) to a much wider set of models. 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. 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. Shun-Ichi Amari, Hiroshi Nagaoka. (RStan lets you use Stan from within R.) Geometry and Data: Manifold Learning and Singular Learning machine-learning algorithms. 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. Methods of Information Geometry. 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. This means we learn Algebra, Geometry, Statistics, and Number Theory in increasing complexity each year. Algebraic Geometry and Statistical Learning Theory. Connections of this type are at the heart of the new field of "algebraic statistics". With the rise of high-dimensional machine learning, these fields are increasing being pulled into interesting computational applications such as manifold learning. Algebraic Geometry and Statistical Learning Theory – Computers. Statistical Methods, 3rd Edition; Academic Press, January 2011. A new open source, software package called Stan lets you fit Bayesian statistical models using HMC. Shastri Anant R., Element of Differential Topology, CRC, February 2011.