A Partial Information Decomposition Based on Causal Tensors
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We propose a partial information decomposition based on the newly introduced framework of causal tensors. The constituting nonnegative information terms follow naturally from this framework, in which the data processing inequality plays a fundamental role. Instead of describing cascades of relations in terms of inequalities, causal tensors allow for a description of cascades in terms of equalities, i.e., exact expressions of the resulting information theoretic divergences is possible. Our approach is firmly rooted in classical information theory, and no new “non-classical information theoretic” measures are needed.
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