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Algebraic Geometry and Statistical Learning Theory
Sure to be influential, Watanabe's 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.
Algebraic Geometry and 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 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.
Mathematical Theory of Bayesian Statistics
Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are ...
Neural information processing
The three volume set LNCS 4232, LNCS 4233, and LNCS 4234 constitutes the refereed proceedings of the 13th International Conference on Neural Information Processing, ICONIP 2006, held in Hong Kong, China in October 2006. The 386 revised full papers presented were carefully reviewed and selected from 1175 submissions.
Neural Information Processing
The three volume set LNCS 4232, LNCS 4233, and LNCS 4234 constitutes the refereed proceedings of the 13th International Conference on Neural Information Processing, ICONIP 2006, held in Hong Kong, China in October 2006. The 386 revised full papers presented were carefully reviewed and selected from 1175 submissions.
Variational Bayesian Learning Theory
This introduction to the theory of variational Bayesian learning summarizes recent developments and suggests practical applications.
Algorithms and Architectures
This volume is the first diverse and comprehensive treatment of algorithms and architectures for the realization of neural network systems. It presents techniques and diverse methods in numerous areas of this broad subject. The book covers major neural network systems structures for achieving effective systems, and illustrates them with examples. This volume includes Radial Basis Function networks, the Expand-and-Truncate Learning algorithm for the synthesis of Three-Layer Threshold Networks, weight initialization, fast and efficient variants of Hamming and Hopfield neural networks, discrete time synchronous multilevel neural systems with reduced VLSI demands, probabilistic design techniques...
Algorithmic Learning Theory
Algorithmic learning theory is mathematics about computer programs which learn from experience. This involves considerable interaction between various mathematical disciplines including theory of computation, statistics, and c- binatorics. There is also considerable interaction with the practical, empirical ?elds of machine and statistical learning in which a principal aim is to predict, from past data about phenomena, useful features of future data from the same phenomena. The papers in this volume cover a broad range of topics of current research in the ?eld of algorithmic learning theory. We have divided the 29 technical, contributed papers in this volume into eight categories (correspond...
Algorithmic Learning Theory
This book constitutes the refereed proceedings of the 16th International Conference on Algorithmic Learning Theory, ALT 2005, held in Singapore in October 2005. The 30 revised full papers presented together with 5 invited papers and an introduction by the editors were carefully reviewed and selected from 98 submissions. The papers are organized in topical sections on kernel-based learning, bayesian and statistical models, PAilearning, query-learning, inductive inference, language learning, learning and logic, learning from expert advice, online learning, defensive forecasting, and teaching.
WAIC and WBIC with Python Stan
Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. The book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in Python and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian sta...
