English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Inferring and comparing complex, multivariable probability density functionsis fundamental to problems in several fields, including probabilistic learning,network theory, and data analysis. Classification and prediction are the twofaces of this class of problem. We take an approach here that simplifies manyaspects of these problems by presenting a structured, series expansion of theKullback-Leibler divergence - a function central to information theory - anddevise a distance metric based on this divergence. Using the M\"obius inversionduality between multivariable entropies and multivariable interactioninformation, we express the divergence as an additive series in the number ofinteracting variables, which provides a restricted and simplified set ofdistributions to use as approximation and with which to model data. Truncationsof this series yield approximations based on the number of interactingvariables. The first few terms of the expansion-truncation are illustrated andshown to lead naturally to familiar approximations, including the well-knownKirkwood superposition approximation. Truncation can also induce a simplerelation between the multi-information and the interaction information. Ameasure of distance between distributions, based on Kullback-Leiblerdivergence, is then described and shown to be a true metric if properlyrestricted. The expansion is shown to generate a hierarchy of metrics andconnects this work to information geometry formalisms. We give an example ofthe application of these metrics to a graph comparision problem that shows thatthe formalism can be applied to a wide range of network problems, provides ageneral approach for systematic approximations in numbers of interactions orconnections, and a related quantitative metric.

Expansion of the Kullback-Leibler Divergence, and a new class of information metrics