Characterizations of matrix and operator-valued &#934;-entropies, and operator Efron-Stein inequalities.

Cheng, Hao-Chung; Hsieh, Min-Hsiu

Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities.

Cheng, Hao-Chung; Hsieh, Min-Hsiu.

Afiliación

Cheng HC; Graduate Institute of Communication Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China; Faculty of Engineering and Information Technology, University of Technology Sydney, 15 Broadway, Ultimo, New South Wales 2007, Australia.
Hsieh MH; Faculty of Engineering and Information Technology , University of Technology Sydney , 15 Broadway, Ultimo, New South Wales 2007, Australia.

Proc Math Phys Eng Sci ; 472(2187): 20150563, 2016 Mar.

Article en En | MEDLINE | ID: mdl-27118909

RESUMEN

We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob.19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix Φ-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued Φ-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.

Palabras clave

EfronStein inequality; matrix concentration inequalities; Φ-entropy

Texto completo

Añadir a Mi BVS

Imprimir

XML

PubMed Links

Buscar en Google

Texto completo: 1 Colección: 01-internacional Base de datos: MEDLINE Aspecto: Determinantes_sociais_saude / Equity_inequality Idioma: En Revista: Proc Math Phys Eng Sci Año: 2016 Tipo del documento: Article País de afiliación: Australia Pais de publicación: Reino Unido

Texto completo

Añadir a Mi BVS

Imprimir

XML

PubMed Links

Buscar en Google