The Minimum Description Length Principle

Voorkant
MIT Press, 2007 - 703 pagina's
1 Reviewen

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.

 

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LibraryThing Review

Gebruikersrecensie  - mdreid - LibraryThing

I have not read this book from cover to cover (and doubt I will) but the sections I have read so far—universal codes, exponential families, and MDL in context—have all been excellent. I would ... Volledige review lezen

Inhoudsopgave

1 Learning Regularity and Compression
3
2 Probabilistic and Statistical Preliminaries
41
3 InformationTheoretic Preliminaries
79
4 InformationTheoretic Properties of Statistical Models
109
5 Crude TwoPart Code MDL
131
P A R T I I Universal Coding
165
6 Universal Coding with Countable Models
171
Normalized Maximum Likelihood
207
P A R T I I I Refined MDL
403
14 MDL Model Selection
409
15 MDL Prediction and Estimation
459
16 MDL Consistency and Convergence
501
17 MDL in Context
523
P A R T I V Additional Background
597
18 The Exponential or Maximum Entropy Families
599
19 InformationTheoretic Properties of Exponential Families
623

Bayes
231
Prequential Plugin
257
TwoPart
271
11 NMLWith Innite Complexity
295
12 Linear Regression
335

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Philosophy of Information

Gedeeltelijke weergave - 2008
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Over de auteur (2007)

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

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