The process of inductive inference -- to infer general laws and principles from particular instances -- is the basis of statistical modeling, pattern recognition, and machine learning. The Minimum Descriptive Length (MDL) principle, a powerful method of inductive inference, holds that the best explanation, given a limited set of observed data, is the one that permits the greatest compression of the data -- that the more we are able to compress the data, the more we learn about the regularities underlying the data. Advances in Minimum Description Length is a sourcebook that will introduce the scientific community to the foundations of MDL, recent theoretical advances, and practical applications. The book begins with an extensive tutorial on MDL, covering its theoretical underpinnings, practical implications as well as its various interpretations, and its underlying philosophy. The tutorial includes a brief history of MDL -- from its roots in the notion of Kolmogorov complexity to the beginning of MDL proper. The book then presents recent theoretical advances, introducing modern MDL methods in a way that is accessible to readers from many different scientific fields. The book concludes with examples of how to apply MDL in research settings that range from bioinformatics and machine learning to psychology. Table of Contents Series Foreword vii Preface ix I Introductory Chapters 1 1 Introducing the Minimum Description Length Principle Peter D. Grunwald 3 2 Minimum Description Length Tutorial Peter D. Grunwald 23 3 MDL, Bayesian Inference, and the Geometry of the Space of Probability Distributions Vijay Balasubramanian 81 4 Hypothesis Testing for Poisson vs. Geometric Distributions Using Stochastic Complexity Aaron D. Lanterman 99 5 Applications of MDL to Selected Families of Models Andrew J. Hanson and Philip Chi-Wing Fu 125 6 Algorithmic Statistics and Kolmogorov's Structure Functions Paul Vitanyi 151 II Theoretical Advances 175 7 Exact Minimax Predictive Density Estimation and MDL Feng Liang and Andrew Barron 177 8 The Contribution of Parameters to Stochastic Complexity Dean P. Foster and Robert A. Stine 195 9 Extended Stochastic Complexity and Its Applications to Learning Kenji Yamanishi 215 10 Kolmogorov's Structure Function in MDL Theory and Lossy Data Compression Jorma Rissanen and Ioan Tabus 245 III Practical Applications 263 11 Minimum Message Length and Generalized Bayesian Nets with Asymmetric Languages Joshua W. Comley and David L. Dowe 265 12 Simultaneous Clustering and Subset Selection via MDL Rebecka Jornsten and Bin Yu 295 13 An MDL Framework for Data Clustering Petri Kontkanen, Petri Myllymaki, Wray Buntine, Jorma Rissanen and Henry Tirri 323 14 Minimum Description Length and Psychological Clustering Models Michael D. Lee and Daniel J. Navarro 355 15 A Minimum Description Length Principle for Perception Nick Chater 385 16 Minimum Description Length and Cognitive Modeling Yong Su, In Jae Myung and Mark A. Pitt 411 Index 435