Daniel Fryer

Daniel Fryer, Inga Strümke, Hien Nguyen

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The Shapley value is provably the only solution concept satisfying these axioms. In this paper, we introduce the Shapley value and draw attention to its recent uses as a feature selection tool. We call into question this use of the Shapley value, using simple, abstract "toy" counterexamples to illustrate that the axioms may work against the goals of feature selection. From this, we develop a number of insights that are then investigated in concrete simulation settings, with a variety of Shapley value formulations, including SHapley Additive exPlanations (SHAP) and Shapley Additive Global importancE (SAGE).

Daniel Fryer, Hien Nguyen, Pascal Castellazzi

We state theoretical properties for $k$-means clustering of Symmetric Positive Definite (SPD) matrices, in a non-Euclidean space, that provides a natural and favourable representation of these data. We then provide a novel application for this method, to time-series clustering of pixels in a sequence of Synthetic Aperture Radar images, via their finite-lag autocovariance matrices.

Daniel Vidali Fryer, Inga Strümke, Hien Nguyen

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.