Polynomial Methods in Statistical Inference : Theory and Practice (Foundations and Trends® in Communications and Information Theory)

Wu, Yihong/ Yang, Pengkun

now publishers Inc（2020/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 198 p.
• 言語 ENG
• 商品コード 9781680837308
• DDC分類 519.54

Full Description

The authors of this monograph survey a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods. These techniques provide useful tools not only for the design of highly practical algorithms with provable optimality, but also for establishing the fundamental limits of inference problems through moment matching. The authors demonstrate the effectiveness of the polynomial method using concrete problems such as entropy and support size estimation, distinct elements problem, and learning Gaussian mixture models. This monograph provides a comprehensive, yet concise, overview of the theory covering topics such as polynomial approximation, polynomial interpolation and majorization, moment space and positive polynomials, orthogonal polynomials and Gaussian quadrature. The authors proceed to show the applications of the theory in statistical inference.

Polynomial Methods in Statistical Inference provides students, and researchers with an accessible and complete treatment of a subject that has recently been used to solve many challenging problems in statistical inference.

Contents

1. Introduction
2. Background
3. Polynomial Approximation Methods
4. Entropy Estimation
5. Estimating the Unseen
6. Mixture Models and Moment Comparison Theorems
7. Learning Gaussian Mixtures
Acknowledgements
References