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

• URL: http://arxiv.org/abs/2007.06011v4
• Date: Sat, 6 Mar 2021 05:46:11 GMT
• Title: Explaining the data or explaining a model? Shapley values that uncover non-linear dependencies
• Authors: Daniel Vidali Fryer, Inga Str\"umke, Hien Nguyen
• Abstract summary: We introduce and demonstrate the use of the energy distance correlations, affine-invariant distance correlation, and Hilbert-Shmidt independence criterion as Shapley value characteristic functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad potential forms of the Shapley value \textit{game formulation}. Amongst the consequences of this flexibility is that there are now many types of Shapley values being discussed, with such variety being a source of potential misunderstanding. To the best of our knowledge, all existing game formulations in the machine learning and statistics literature fall into a category which we name the model-dependent category of game formulations. In this work, we consider an alternative and novel formulation which leads to the first instance of what we call model-independent Shapley values. These Shapley values use a (non-parametric) measure of non-linear dependence as the characteristic function. The strength of these Shapley values is in their ability to uncover and attribute non-linear dependencies amongst features. We introduce and demonstrate the use of the energy distance correlations, affine-invariant distance correlation, and Hilbert-Shmidt independence criterion as Shapley value characteristic functions. In particular, we demonstrate their potential value for exploratory data analysis and model diagnostics. We conclude with an interesting expository application to a classical medical survey data set.

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