Explaining the data or explaining a model? Shapley values that uncover non-linear dependencies
This work addresses the need for better interpretability tools in machine learning by providing a novel approach to feature attribution that is independent of specific models, though it is incremental in expanding the Shapley value framework.
The paper tackles the problem of explaining data dependencies rather than model predictions by introducing model-independent Shapley values that use non-linear dependence measures as characteristic functions, resulting in a method that uncovers and attributes non-linear dependencies among features for exploratory data analysis and model diagnostics.
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.