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This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.
No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
This volume reviews the challenges and alternative approaches to modeling how individuals change across time and provides methodologies and data analytic strategies for behavioral and social science researchers. This accessible guide provides concrete, clear examples of how contextual factors can be included in most research studies. Each chapter can be understood independently, allowing readers to first focus on areas most relevant to their work. The opening chapter demonstrates the various ways contextual factors are represented—as covariates, predictors, outcomes, moderators, mediators, or mediated effects. Succeeding chapters review "best practice" techniques for treating missing data, making model comparisons, and scaling across developmental age ranges. Other chapters focus on specific statistical techniques such as multilevel modeling and multiple-group and multilevel SEM, and how to incorporate tests of mediation, moderation, and moderated mediation. Critical measurement and theoretical issues are discussed, particularly how age can be represented and the ways in which context can be conceptualized. The final chapter provides a compelling call to include contextual factors in theorizing and research. This book will appeal to researchers and advanced students conducting developmental, social, clinical, or educational research, as well as those in related areas such as psychology and linguistics.
This book constitutes the refereed proceedings of the 8th International Conference, MLDM 2012, held in Berlin, Germany in July 2012. The 51 revised full papers presented were carefully reviewed and selected from 212 submissions. The topics range from theoretical topics for classification, clustering, association rule and pattern mining to specific data mining methods for the different multimedia data types such as image mining, text mining, video mining and web mining.
Data mining applications range from commercial to social domains, with novel applications appearing swiftly; for example, within the context of social networks. The expanding application sphere and social reach of advanced data mining raise pertinent issues of privacy and security. Present-day data mining is a progressive multidisciplinary endeavor. This inter- and multidisciplinary approach is well reflected within the field of information systems. The information systems research addresses software and hardware requirements for supporting computationally and data-intensive applications. Furthermore, it encompasses analyzing system and data aspects, and all manual or automated activities. In that respect, research at the interface of information systems and data mining has significant potential to produce actionable knowledge vital for corporate decision-making. The aim of the proposed volume is to provide a balanced treatment of the latest advances and developments in data mining; in particular, exploring synergies at the intersection with information systems. It will serve as a platform for academics and practitioners to highlight their recent achievements and reveal potential opportunities in the field. Thanks to its multidisciplinary nature, the volume is expected to become a vital resource for a broad readership ranging from students, throughout engineers and developers, to researchers and academics.
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 22nd International Conference on Formal Grammar, FG 2017, collocated with the European Summer School in Logic, Language and Information in July 2017. The 9 contributed papers were carefully reviewed and selected from 14 submissions. The focus of papers are as follows: Formal and computational phonology, morphology, syntax, semantics and pragmatics Model-theoretic and proof-theoretic methods in linguistics Logical aspects of linguistic structure Constraint-based and resource-sensitive approaches to grammar Learnability of formal grammar Integration of stochastic and symbolic models of grammar Foundational, methodological and architectural issues in grammar and linguistics Mathematical foundations of statistical approaches to linguistic analysis