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Item type:Publication, Access status: without files , 43 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Information decomposition based on cooperative game theory(2021); ; 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 Article44 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Discriminating between causal structures in bayesian networks given partial observations(2014); ; Given a fixed dependency graph G that describes a Bayesian network of binary variables X1, Xn, our main result is a tight bound on P the mutual information Ic(Y1, Yk) Σkj=1 H(Yj)/c - H(Y1, Yk) of an observed subset Y1, Yk of the variables X1, Xn. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in G. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.Publicationtype: Journal Article18 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On solution sets of information inequalities(2012-12-14); We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.Publicationtype: Journal Article16