Lossy asymptotic equipartition property for hierarchical data structures

Kwabena Doku-Amponsah

doi:10.17654/MS101051013

Lossy asymptotic equipartition property for hierarchical data structures

Kwabena Doku-Amponsah

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper presents a rate-distortion theory for hierarchically networked data structures modelled as tree-indexed multitype process. Specifically, this paper gives a generalized asymptotic equipartition property (AEP) for hierarchical data structures. The proof of our main result uses large deviation principles for suitably defined empirical measures of multitype Galton-Watson trees.

Original language	English
Pages (from-to)	1013-1024
Number of pages	12
Journal	Far East Journal of Mathematical Sciences
Volume	101
Issue number	5
DOIs	https://doi.org/10.17654/MS101051013
Publication status	Published - Mar 2017

Keywords

Asymptotic equipartition property
Empirical measure
Perron-Frobenius eigenvalue
Perron-Frobenius eigenvector
Rate-distortion theory
Relative entropy
Weak irreducibility

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10.17654/MS101051013

Cite this

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title = "Lossy asymptotic equipartition property for hierarchical data structures",

abstract = "This paper presents a rate-distortion theory for hierarchically networked data structures modelled as tree-indexed multitype process. Specifically, this paper gives a generalized asymptotic equipartition property (AEP) for hierarchical data structures. The proof of our main result uses large deviation principles for suitably defined empirical measures of multitype Galton-Watson trees.",

keywords = "Asymptotic equipartition property, Empirical measure, Perron-Frobenius eigenvalue, Perron-Frobenius eigenvector, Rate-distortion theory, Relative entropy, Weak irreducibility",

author = "Kwabena Doku-Amponsah",

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AB - This paper presents a rate-distortion theory for hierarchically networked data structures modelled as tree-indexed multitype process. Specifically, this paper gives a generalized asymptotic equipartition property (AEP) for hierarchical data structures. The proof of our main result uses large deviation principles for suitably defined empirical measures of multitype Galton-Watson trees.

KW - Asymptotic equipartition property

KW - Empirical measure

KW - Perron-Frobenius eigenvalue

KW - Perron-Frobenius eigenvector

KW - Rate-distortion theory

KW - Relative entropy

KW - Weak irreducibility

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JF - Far East Journal of Mathematical Sciences

IS - 5

ER -

Lossy asymptotic equipartition property for hierarchical data structures

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Keywords

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