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

Modern statistical modeling is an important complement to the moretraditional approach of physics where Complex Systems are studied by means ofextremely simple idealized models. The Minimum Description Length (MDL) is aprincipled approach to statistical modeling combining Occam's razor withInformation Theory for the selection of models providing the most concisedescriptions. In this work, we introduce the Boltzmannian MDL (BMDL), aformalization of the principle of MDL with a parametric complexity convenientlyformulated as the free-energy of an artificial thermodynamic system. In thisway, we leverage on the rich theoretical and technical background ofstatistical mechanics, to show the crucial importance that phase transitionsand other thermodynamic concepts have on the problem of statistical modelingfrom an information theoretic point of view. For example, we provideinformation theoretic justifications of why a high-temperature series expansioncan be used to compute systematic approximations of the BMDL when the formalismis used to model data, and why statistically significant model selections canbe identified with ordered phases when the BMDL is used to model models. Totest the introduced formalism, we compute approximations of BMDL for theproblem of community detection in complex networks, where we obtain aprincipled MDL derivation of the Girvan-Newman (GN) modularity and theZhang-Moore (ZM) community detection method. Here, by means of analyticalestimations and numerical experiments on synthetic and empirical networks, wefind that BMDL-based correction terms of the GN modularity improve the qualityof the detected communities and we also find an information theoreticjustification of why the ZM criterion for estimation of the number of networkcommunities is better than alternative approaches such as the bare minimizationof a free energy.

Thermodynamics of the Minimum Description Length on Community Detection