The Minimum Message Length (MML) Principle is an information-theoretic approach to induction, hypothesis testing, model selection, and statistical inference. MML, which provides a formal specification for the implementation of Occam's Razor, asserts that the ‘best’ explanation of observed data is the shortest. Further, an explanation is acceptable (i.e. the induction is justified) only if the explanation is shorter than the original data. This book gives a sound introduction to the Minimum Message Length Principle and its applications, provides the theoretical arguments for the adoption of the principle, and shows the development of certain approximations that assist its practical application. MML appears also to provide both a normative and a descriptive basis for inductive reasoning generally, and scientific induction in particular. The book describes this basis and aims to show its relevance to the Philosophy of Science. Statistical and Inductive Inference by Minimum Message Length will be of special interest to graduate students and researchers in Machine Learning and Data Mining, scientists and analysts in various disciplines wishing to make use of computer techniques for hypothesis discovery, statisticians and econometricians interested in the underlying theory of their discipline, and persons interested in the Philosophy of Science. The book could also be used in a graduate-level course in Machine Learning and Estimation and Model-selection, Econometrics and Data Mining. C.S. Wallace was appointed Foundation Chair of Computer Science at Monash University in 1968, at the age of 35, where he worked until his death in 2004. He received an ACM Fellowship in 1995, and was appointed Professor Emeritus in 1996. Professor Wallace made numerous significant contributions to diverse areas of Computer Science, such as Computer Architecture, Simulation and Machine Learning. His final research focused primarily on the Minimum Message Length Principle.

Mythanksareduetothemanypeoplewhohaveassistedintheworkreported here and in the preparation of this book. The work is incomplete and this account of it rougher than it might be. Such virtues as it has owe much to others; the faults are all mine. MyworkleadingtothisbookbeganwhenDavidBoultonandIattempted to develop a method for intrinsic classi?cation. Given data on a sample from some population, we aimed to discover whether the population should be considered to be a mixture of di?erent types, classes or species of thing, and, if so, how many classes were present, what each class looked like, and which things in the sample belonged to which class. I saw the problem as one of Bayesian inference, but with prior probability densities replaced by discrete probabilities re?ecting the precision to which the data would allow parameters to be estimated. Boulton, however, proposed that a classi?cation of the sample was a way of brie?y encoding the data: once each class was described and each thing assigned to a class, the data for a thing would be partially implied by the characteristics of its class, and hence require little further description. After some weeks’ arguing our cases, we decided on the maths for each approach, and soon discovered they gave essentially the same results. Without Boulton’s insight, we may never have made the connection between inference and brief encoding, which is the heart of this work.

This book explores inductive inference using the minimum message length (MML) principle, a Bayesian method which is a realisation of Ockham's Razor based on information theory. Accompanied by a library of software, the book can assist an applications programmer, student or researcher in the fields of data analysis and machine learning to write computer programs based upon this principle. MML inference has been around for 50 years and yet only one highly technical book has been written about the subject. The majority of research in the field has been backed by specialised one-off programs but this book includes a library of general MML-based software, in Java. The Java source code is available under the GNU GPL open-source license. The software library is documented using Javadoc which produces extensive cross referenced HTML manual pages. Every probability distribution and statistical model that is described in the book is implemented and documented in the software library. The library may contain a component that directly solves a reader's inference problem, or contain components that can be put together to solve the problem, or provide a standard interface under which a new component can be written to solve the problem. This book will be of interest to application developers in the fields of machine learning and statistics as well as academics, postdocs, programmers and data scientists. It could also be used by third year or fourth year undergraduate or postgraduate students.

A comprehensive introduction and reference guide to the minimum description length (MDL) Principle that is accessible to researchers dealing with inductive reference in diverse areas including statistics, pattern classification, machine learning, data mining, biology, econometrics, and experimental psychology, as well as philosophers interested in the foundations of statistics. The minimum description length (MDL) principle is a powerful method of inductive inference, the basis of statistical modeling, pattern recognition, and machine learning. It holds that the best explanation, given a limited set of observed data, is the one that permits the greatest compression of the data. MDL methods are particularly well-suited for dealing with model selection, prediction, and estimation problems in situations where the models under consideration can be arbitrarily complex, and overfitting the data is a serious concern. This extensive, step-by-step introduction to the MDL Principle provides a comprehensive reference (with an emphasis on conceptual issues) that is accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection, including biology, econometrics, and experimental psychology. Part I provides a basic introduction to MDL and an overview of the concepts in statistics and information theory needed to understand MDL. Part II treats universal coding, the information-theoretic notion on which MDL is built, and part III gives a formal treatment of MDL theory as a theory of inductive inference based on universal coding. Part IV provides a comprehensive overview of the statistical theory of exponential families with an emphasis on their information-theoretic properties. The text includes a number of summaries, paragraphs offering the reader a "fast track" through the material, and boxes highlighting the most important concepts.

This book is the first cohesive treatment of ITL algorithms to adapt linear or nonlinear learning machines both in supervised and unsupervised paradigms. It compares the performance of ITL algorithms with the second order counterparts in many applications.

Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff (1926-2009), honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines (UTMs) could be used for universal Bayesian prediction and artificial intelligence (machine learning). This work continues to increasingly influence and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of (general) intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy.