Lossy Asymptotic Equipartition property for Hierarchical Data Structures

TL;DR

This paper develops a rate-distortion theory for hierarchical tree-structured data, establishing a generalized asymptotic equipartition property using large deviation principles for multitype Galton-Watson trees.

Contribution

It introduces a novel AEP for hierarchical data modeled as multitype processes, extending classical information theory to complex networked structures.

Findings

Generalized AEP for hierarchical data structures

Application of large deviation principles to process-level measures

Framework for rate-distortion analysis of tree-indexed processes

Abstract

This paper presents a rate-distortion theory for hierarchical networked data structures modelled as tree-indexed multitype process. To be specific, this paper gives a generalized Asymptotic Equipartition Property (AEP) for the Process. The general methodology of proof of the AEP are process level large deviation principles for suitably defined empirical measures for muiltitype Galton-Watson trees.