By Peter D. Grünwald

The minimal description size (MDL) precept is a strong approach to inductive inference, the foundation of statistical modeling, trend attractiveness, and computer studying. It holds that the simplest rationalization, given a constrained set of saw facts, is the person who allows the best compression of the information. MDL equipment are rather well-suited for facing version choice, prediction, and estimation difficulties in events the place the versions into account might be arbitrarily advanced, and overfitting the information is a major concern.This broad, step by step advent to the MDL precept presents a complete reference (with an emphasis on conceptual concerns) that's available to graduate scholars and researchers in information, development class, laptop studying, and knowledge mining, to philosophers drawn to the principles of information, and to researchers in different technologies that contain version choice, together with biology, econometrics, and experimental psychology. half I offers a simple creation to MDL and an outline of the options in facts and knowledge concept had to comprehend MDL. half II treats common coding, the information-theoretic proposal on which MDL is outfitted, and half III supplies a proper remedy of MDL idea as a idea of inductive inference in keeping with common coding. half IV presents a finished evaluation of the statistical concept of exponential households with an emphasis on their information-theoretic homes. The textual content incorporates a variety of summaries, paragraphs providing the reader a "fast tune" throughout the fabric, and containers highlighting crucial innovations.

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**Extra resources for The Minimum Description Length Principle (Adaptive Computation and Machine Learning) **

**Example text**

Such a description should always uniquely specify the data it describes - hence given a description or 1. Unless we call “generated by a fair coin toss” a “regularity” too. There is nothing wrong with that view - the point is that, the more we can compress a sequence, the more regularity we have found. One can avoid all terminological confusion about the concept of “regularity” by making it relative to something called a “base measure,” but that is beyond the scope of this book (Li and Vitányi 1997).

Of course, the description was done using natural language and we may want to do it in some more formal manner. If we want to identify regularity with compressibility, then it should also be the case that nonregular sequences can not be compressed. 2) has been generated by fair coin tosses, it should not be compressible. 2) itself. 3). Therefore, it does not count as a “real” description: one cannot regenerate the whole sequence if one has the description. 3) is one of those sequences of 10000 bits in which there are four times as many 0s as there are 1s.

G. g. a particular polynomial). In parametric inference (Chapter 2), a point hypothesis corresponds to a particular parameter value. A point hypothesis may also be viewed as an instantiation of a model. 3, page 62 where we give several examples to clarify our terminology. 2 Models and Model Classes; (Point) Hypotheses. codes (description methods) giving rise to lengths L(D|H) and L(H). We now discuss these codes in more detail. We will see that the deﬁnition of L(H) is problematic, indicating that we somehow need to “reﬁne” our crude MDL principle.