Partial information decomposition

In 2010, a shy arXiv paper appeared which caused a splash in the then-small information complexity community. This paper by Williams and Beer introduced the mathematical framework of Partial Information Decomposition (PID). PID, while not the first attempt at decomposing multivariate information, was extremely ingenious, and a few showcases of PID shedding light on other information-theoretic problems soon appeared.

I am fascinated by the topic of information decomposition in general, and PID in particular. Of the many possibilities offered by this framework, I am particularly interested in the notion of synergy: information that can be obtained from a set of several variables, but not from each one of them separately. I believe the concept of synergy and the mathematics of PID hold very valuable ideas to contribute to a formal theory of complexity.

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