In recent years, machine learning has shown great promise in a variety of real-world applications.

We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs.

Machine learning (ML) algorithms can solve many prediction tasks with greater accuracy than classical methods.

The Shapley framework for explainability has strength in its general applicability combined with its precise, rigorous foundation: it provides a common, model-agnostic language for AI explainability and uniquely satisfies a set of intuitive mathematical axioms. However, Shapley values are too restrictive in one significant regard: they ignore all causal structure in the data.

The critical challenge when using the Shapley value is its well-known computational intractability.

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning settings, leading to unintuitive model interpretation. In particular, the Shapley value uses the same weight for all marginal contributions---i.e. it gives the same importance when a large number of other features are given versus when a small number of other features are given. This property can be problematic if larger feature sets are more or less informative than smaller feature sets. Our work performs a rigorous analysis of the potential limitations of Shapley feature attribution. We identify simple settings where the Shapley value is mathematically suboptimal by assigning larger attributions for less influential features. Motivated by this observation, we propose WeightedSHAP, which generalizes the Shapley value and learns which marginal contributions to focus directly from data. On several real-world datasets, we demonstrate that the influential features identified by WeightedSHAP are better able to recapitulate the model's predictions compared to the features identified by the Shapley value.

Popular feature importance techniques compute additive approximations to nonlinear models by first defining a cooperative game describing the value of different subsets of the model's features, then calculating the resulting game's Shapley values to attribute credit additively between the features. However, the specific modeling settings in which the Shapley values are a poor approximation for the true game have not been well-described. In this paper we utilize an interpretation of Shapley values as the result of an orthogonal projection between vector spaces to calculate a residual representing the kernel component of that projection. We provide an algorithm for computing these residuals, characterize different modeling settings based on the value of the residuals, and demonstrate that they capture information about model predictions that Shapley values cannot. Shapley residuals can thus act as a warning to practitioners against overestimating the degree to which Shapley-value-based explanations give them insight into a model.

Explaining machine learning models is an important and increasingly popular area of research interest. The Shapley value from game theory has been proposed as a prime approach to compute feature importance towards model predictions on images, text, tabular data, and recently graph neural networks (GNNs) on graphs. In this work, we revisit the appropriateness of the Shapley value for GNN explanation, where the task is to identify the most important subgraph and constituent nodes for GNN predictions. We claim that the Shapley value is a non-ideal choice for graph data because it is by definition not structure-aware. We propose a Graph Structure-aware eXplanation (GStarX) method to leverage the critical graph structure information to improve the explanation. Specifically, we define a scoring function based on a new structure-aware value from the cooperative game theory proposed by Hamiache and Navarro (HN). When used to score node importance, the HN value utilizes graph structures to attribute cooperation surplus between neighbor nodes, resembling message passing in GNNs, so that node importance scores reflect not only the node feature importance, but also the node structural roles. We demonstrate that GStarX produces qualitatively more intuitive explanations, and quantitatively improves explanation fidelity over strong baselines on chemical graph property prediction and text graph sentiment classification.

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values (SV), a coalition game theoretical framework that has previously been applied to different machine learning model interpretation tasks, such as linear models, tree ensembles and deep networks. By analysing SVs from a functional perspective, we propose RKHS-SHAP, an attribution method for kernel machines that can efficiently compute both Interventional and Observational Shapley values using kernel mean embeddings of distributions. We show theoretically that our method is robust with respect to local perturbations - a key yet often overlooked desideratum for consistent model interpretation. Further, we propose Shapley regulariser, applicable to a general empirical risk minimisation framework, allowing learning while controlling the level of specific feature's contributions to the model. We demonstrate that the Shapley regulariser enables learning which is robust to covariate shift of a given feature and fair learning which controls the SVs of sensitive features.