Advances in Minimum Description Length: Theory and Applications

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Overview

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 MDLin research settings that range from bioinformatics and machine learning to psychology.

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Product Details

Meet the Author

Peter D. Grünwald is a researcher at CWI, the National Research Institute for Mathematics andComputer Science, Amsterdam, the Netherlands. He is also affiliated with EURANDOM, the EuropeanResearch Institute for the Study of Stochastic Phenomena, Eindhoven, the Netherlands.

Mark A. Pitt is Professor in the Department of Psychology and a member of the Center forCognitive Science at Ohio State University.

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Table of Contents

1 Introducing the minimum description length principle 3
2 Minimum description length tutorial 23
3 MDL, Bayesian inference, and the geometry of the space of probability distributions 81
4 Hypothesis testing for Poisson vs. geometric distributions using stochastic complexity 99
5 Applications of MDL to selected families of models 125
6 Algorithmic statistics and Kolmogorov's structure functions 151
7 Exact minimax predictive density estimation and MDL 177
8 The contribution of parameters to stochastic complexity 195
9 Extended stochastic complexity and its applications to learning 215
10 Kolmogorov's structure function in MDL theory and lossy data compression 245
11 Minimum message length and generalized Bayesian nets with asymmetric languages 265
12 Simultaneous clustering and subset selection via MDL 295
13 An MDL framework for data clustering 323
14 Minimum description length and psychological clustering models 355
15 A minimum description length principle for perception 385
16 Minimum description length and cognitive modeling 411
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