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Shapley values have become increasingly popular in the machine learningliterature thanks to their attractive axiomatisation, flexibility, anduniqueness in satisfying certain notions of `fairness'. The flexibility arisesfrom the myriad potential forms of the Shapley value \textit{game formulation}.Amongst the consequences of this flexibility is that there are now many typesof Shapley values being discussed, with such variety being a source ofpotential misunderstanding. To the best of our knowledge, all existing gameformulations in the machine learning and statistics literature fall into acategory which we name the model-dependent category of game formulations. Inthis work, we consider an alternative and novel formulation which leads to thefirst instance of what we call model-independent Shapley values. These Shapleyvalues use a (non-parametric) measure of non-linear dependence as thecharacteristic function. The strength of these Shapley values is in theirability to uncover and attribute non-linear dependencies amongst features. Weintroduce and demonstrate the use of the energy distance correlations,affine-invariant distance correlation, and Hilbert-Shmidt independencecriterion as Shapley value characteristic functions. In particular, wedemonstrate their potential value for exploratory data analysis and modeldiagnostics. We conclude with an interesting expository application to aclassical medical survey data set.

Explaining the data or explaining a model? Shapley values that uncover non-linear dependencies