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    Item type:Publication, Access status: without files ,
    Information decomposition based on cooperative game theory
    (2021)
    Ay, Nihat
    ;
    Polani, Daniel
    ;
    Virgo, Nathaniel
    We offer a new approach to the information decomposition problem in information theory: given a target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative terms that quantify the contributions of each random variable, not only individually but also in combination? We define a new way to decompose the mutual information, which we call the Information Attribution (IA), and derive a solution using cooperative game theory. It can be seen as assigning a share" of the mutual information to each combination of the source variables. Our decomposition is based on a different lattice from the usual partial information decomposition' (PID) approach, and as a consequence the IA has a smaller number of terms than PID: it has analogs of the synergy and unique information terms, but lacks separate terms corresponding to redundancy, instead sharing redundant information between the unique information terms. Because of this, it is able to obey equivalents of the axioms known as local positivity' and identity', which cannot be simultaneously satisfied by a PID measure.
    Publicationtype: Journal Article
      44
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    Item type:Publication, Access status: without files ,
    Zipf's law: Balancing signal usage cost and communication efficiency
    (Public Library of Science (PLoS), 2015-10-01)
    Salge, Christoph
    ;
    Ay, Nihat
    ;
    Polani, Daniel
    ;
    Prokopenko, Mikhail
    We propose a model that explains the reliable emergence of power laws (e.g., Zipf's law) during the development of different human languages. The model incorporates the principle of least effort in communications, minimizing a combination of the information-Theoretic communication inefficiency and direct signal cost. We prove a general relationship, for all optimal languages, between the signal cost distribution and the resulting distribution of signals. Zipf's law then emerges for logarithmic signal cost distributions, which is the cost distribution expected for words constructed from letters or phonemes.
    Publicationtype: Journal Article
    Scopus© Citations 14  18