Algebraic Geometry and Statistical Learning Theory [Hardcover]

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory.Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.Sure to be influential, Watanabes book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.Preface; 1. Introduction; 2. Singularity theory; 3. Algebraic geometry; 4. Zeta functions and singular integral; 5. Empirical processes; 6. Singular learning theory; 7. Singular learning machines; 8. Singular information science; Bibliography; Index. Overall, the many insightful remarks and simple direct language make the book a pleasure to read.
Shaowei Lin, Mathematical Reviews