Universal Coding and Order Identification by Model Selection Methods. 1st ed. 2018

種類:

電子ブック

責任表示:

by Élisabeth Gassiat

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Gassiat, Élisabeth.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783319962627 [3319962620]    

注記:

1. Lossless Coding -- 2.Universal Coding on Finite Alphabets -- 3.Universal Coding on Infinite Alphabets -- 4.Model Order Estimation -- Notation -- Index.
The purpose of these notes is to highlight the far-reaching connections between Information Theory and Statistics. Universal coding and adaptive compression are indeed closely related to statistical inference concerning processes and using maximum likelihood or Bayesian methods. The book is divided into four chapters, the first of which introduces readers to lossless coding, provides an intrinsic lower bound on the codeword length in terms of Shannon’s entropy, and presents some coding methods that can achieve this lower bound, provided the source distribution is known. In turn, Chapter 2 addresses universal coding on finite alphabets, and seeks to find coding procedures that can achieve the optimal compression rate, regardless of the source distribution. It also quantifies the speed of convergence of the compression rate to the source entropy rate. These powerful results do not extend to infinite alphabets. In Chapter 3, it is shown that there are no universal codes over the class of stationary ergodic sourc

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