Probability Statistics

Advances in Minimum Description Length: Theory and by Peter D. Grunwald, In Jae Myung, Mark A. Pitt

By Peter D. Grunwald, In Jae Myung, Mark A. Pitt

The strategy of inductive inference -- to deduce basic legislation and ideas from specific situations -- is the root of statistical modeling, development popularity, and desktop studying. The minimal Descriptive size (MDL) precept, a strong approach to inductive inference, holds that the simplest rationalization, given a restricted set of saw information, is the one who allows the best compression of the information -- that the extra we can compress the knowledge, the extra we know about the regularities underlying the knowledge. Advances in minimal Description size is a sourcebook that may introduce the medical neighborhood to the principles of MDL, fresh theoretical advances, and useful applications.The booklet starts with an in depth educational on MDL, overlaying its theoretical underpinnings, sensible implications in addition to its a number of interpretations, and its underlying philosophy. the academic features a short historical past of MDL -- from its roots within the proposal of Kolmogorov complexity to the start of MDL right. The publication then offers contemporary theoretical advances, introducing smooth MDL equipment in a manner that's available to readers from many various medical fields. The e-book concludes with examples of the way to use MDL in examine settings that diversity from bioinformatics and computer studying to psychology.

Show description

Read Online or Download Advances in Minimum Description Length: Theory and Applications (Neural Information Processing series) PDF

Similar probability & statistics books

Discriminant Analysis and Statistical Pattern Recognition

The Wiley-Interscience Paperback sequence involves chosen books which have been made extra available to shoppers which will bring up worldwide allure and common circulate. With those new unabridged softcover volumes, Wiley hopes to increase the lives of those works by means of making them to be had to destiny generations of statisticians, mathematicians, and scientists.

Basic Statistics: Tales of Distributions

Research statistical reasoning and challenge fixing from a best-selling writer who makes use of a wealth of examples from the social and behavioral sciences,, education,, nursing/allied overall healthiness, and company fields--as good as examples from daily life-to assist you study and comprehend. Praised for his transparent motives, Spatz exhibits you the way to begin with a knowledge set, establish the questions it poses, make certain and perform statistical approaches, and utilizing simple English, inform the tale the information demonstrate.

Nonparametrics: Statistical Methods Based on Ranks

Rank checks are a category of statistical approaches that mix nice simplicity with spectacular strength. This reprint of a vintage reference ebook bargains an intensive description of those checks and the estimating strategies derived from them, and offers an account in their houses. even though the sphere of rank exams has noticeable little swap, vital new methodologies have sprung up that still serve the aim of releasing information from the unrealistic version assumptions that so often invalidate its purposes.

Classical and Spatial Stochastic Processes: With Applications to Biology

The revised and multiplied variation of this textbook provides the techniques and functions of random methods with an analogous illuminating simplicity as its first version, yet with the outstanding addition of considerable sleek fabric on organic modeling. whereas nonetheless treating many very important difficulties in fields equivalent to engineering and mathematical physics, the ebook additionally specializes in the hugely appropriate issues of cancerous mutations, influenza evolution, drug resistance, and immune reaction.

Extra info for Advances in Minimum Description Length: Theory and Applications (Neural Information Processing series)

Sample text

A good understanding of this relationship is essential for a good understanding of MDL. 1 introduces prefix codes, the type of codes we work with in MDL. 1 Information Theory I: Probabilities and Code Lengths 25 are related to probability distributions in two ways. 2 we discuss the first relationship, which is related to the Kraft inequality: for every probability mass function P , there exists a code with lengths − log P , and vice versa. 3 discusses the second relationship, related to the information inequality, which says that if the data are distributed according to P , then the code with lengths − log P achieves the minimum expected code length.

9} L such that Lj (xn ) = minL∈L L(xn ), using a uniform code. This takes log 9 bits. We then encode xn itself using the code indexed by j. This takes Lj bits. 9, the resulting scheme properly defines a prefix code: a decoder can decode xn by first decoding j, and then decoding xn using Lj . Thus, for every possible xn ∈ X n , we obtain ¯ 2-p (xn ) = min L(xn ) + log 9. 15n. Unless n is very small, no matter what xn arises, the extra ˆ n ) is negligible. ¯ 2-p compared to L(x number of bits we need using L More generally, let L = {L1 , .

Connectionist, Statistical and Symbolic Approaches to Learning for Natural Language Processing, Volume 1040 in Springer Lecture Notes in Artificial Intelligence, pp. 203–216. Berlin: Springer-Verlag Kolmogorov, A. (1965). Three approaches to the quantitative definition of information. Problems of Information Transmission, 1 (1), 1–7. , and P. Vit´ anyi (1997). An Introduction to Kolmogorov Complexity and Its Applications, 2nd edition. New York: Springer-Verlag. , V. A. Pitt (2000). Counting probability distributions: Differential geometry and model selection.

Download PDF sample

Rated 4.04 of 5 – based on 26 votes