Relationships Between Local Intrinsic Dimensionality and Tail Entropy

Bailey, James E.; Houle, Michael E.; Ma, Xingjun

doi:10.1007/978-3-030-89657-7_15

Cited by 2 publications

(5 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we note that this work considerably expands a recent study by Bailey et al [ 3 ], which established relationships between tail entropies and LID. This current paper extends and generalizes that work in several directions: (i) We establish general lemmas that provide sufficient conditions for when it is possible to substitute a tail distribution with components such as a power law, inside an integral.…”

Section: Related Worksupporting

confidence: 79%

“…This current paper extends and generalizes that work in several directions: (i) We establish general lemmas that provide sufficient conditions for when it is possible to substitute a tail distribution with components such as a power law, inside an integral. The techniques of [ 3 ] were specially crafted for specific integrals. (ii) We provide results for statistical divergences and distances (the work of [ 3 ] only considers entropy).…”

Section: Related Workmentioning

confidence: 99%

“…The techniques of [ 3 ] were specially crafted for specific integrals. (ii) We provide results for statistical divergences and distances (the work of [ 3 ] only considers entropy). (iii) We show how to formulate results for the multivariate context (as [ 3 ] only considers univariate scenarios).…”

Section: Related Workmentioning

confidence: 99%

“…In summary, our key contributions are the development of substantial new theory that asymptotically relates tail entropy, divergences and LID. It builds on and extends an earlier work by Bailey et al [ 3 ], which focused solely on univariate entropies, without reference to divergences or multivariate settings. Specifically in this paper, we: Formulate technical lemmas which delineate when it is possible to substitute certain types of tail distributions by simple formulations that depend only on their associated LID values.…”

Section: Introductionmentioning

confidence: 96%

“…Our focus in this paper is to characterize entropy and statistical divergences at a highly local scale, for an asymptotically small vicinity around a specified location. We show that it is possible to leverage properties that arise from LID based characterizations of lower tail distributions [ 3 ], to develop analytical expressions for a wide selection of entropy variants and statistical divergences, in both univariate and multivariate settings. This yields expressions for tail entropies and tail divergences .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Local Intrinsic Dimensionality, Entropy and Statistical Divergences

Bailey

Houle

2022

Entropy

Self Cite

View full text Add to dashboard Cite

Properties of data distributions can be assessed at both global and local scales. At a highly localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which assesses growth rates of the cumulative distribution function within a restricted neighborhood and characterizes properties of the geometry of a local neighborhood. In this paper, we explore the connection of LID to other well known measures for complexity assessment and comparison, namely, entropy and statistical distances or divergences. In an asymptotic context, we develop analytical new expressions for these quantities in terms of LID. This reveals the fundamental nature of LID as a building block for characterizing and comparing data distributions, opening the door to new methods for distributional analysis at a local scale.

show abstract

Section: Related Worksupporting

confidence: 79%

Section: Related Workmentioning

confidence: 99%