  Despite their ubiquitous use, Shapley value feature attributions can be
misleading due to feature interaction in both model and data. We propose an
alternative attribution approach, Shapley Sets, which awards value to sets of
features. Shapley Sets decomposes the underlying model into non-separable
variable groups using a recursive function decomposition algorithm with log
linear complexity in the number of variables. Shapley Sets attributes to each
non-separable variable group their combined value for a particular prediction.
We show that Shapley Sets is equivalent to the Shapley value over the
transformed feature set and thus benefits from the same axioms of fairness.
Shapley Sets is value function agnostic and we show theoretically and
experimentally how Shapley Sets avoids pitfalls associated with Shapley value
based alternatives and are particularly advantageous for data types with
complex dependency structure.
