Abstract
Partial information decomposition (PID) separates the contributions of sources about a target into unique, redundant, and synergistic components of information. In essence, PID answers the question of “who knows what” of a system of random variables and hence has applications to a wide spectrum of fields ranging from social to biological sciences. The paper presents MaxEnt3D_Pid, an algorithm that computes the PID of three sources, based on a recently-proposed maximum entropy measure, using convex optimization (cone programming). We describe the algorithm and its associated software utilization and report the results of various experiments assessing its accuracy. Moreover, the paper shows that a hierarchy of bivariate and trivariate PID allows obtaining the finer quantities of the trivariate partial information measure.
Highlights
Motivation and SignificanceThe characterization of dependencies within complex multivariate systems helps to identify the mechanisms operating in the system and understanding their function
The work of Williams and Beer [6,7] introduced a framework, called partial information decomposition (PID), which quantifies whether different input variables provide redundant, unique, or synergistic information about an output variable when combined with other input variables
We presented M AX E NT 3D_P ID, a Python module that computes a trivariate decomposition based on the partial information decomposition (PID) framework of Williams and
Summary
The characterization of dependencies within complex multivariate systems helps to identify the mechanisms operating in the system and understanding their function. From a practical point of view, the trivariate PID allows studying new types of distributed information that only appear beyond the bivariate case, such as information that is redundant for two inputs and unique with respect to a third [6] This extension is significant both to study multivariate systems directly, as well as to be exploited for data analysis [21,44]. The quantification of multivariate redundancy can be applied to dimensionality reduction [22] or to better understand how representations emerge in neural networks during learning [49,50] This software promises to contribute significantly to the refinement of the information-theoretic tools it implements and to foster its widespread application to analyze data from multivariate systems
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