The use of algorithm-agnostic approaches is an emerging area of research for explaining the contribution of individual features towards the predicted outcome. Whilst there is a focus on explaining the prediction itself, a little has been done on explaining the robustness of these models, that is, how each feature contributes towards achieving that robustness. In this paper, we propose the use of Shapley values to explain the contribution of each feature towards the model's robustness, measured in terms of Receiver-operating Characteristics (ROC) curve and the Area under the ROC curve (AUC). With the help of an illustrative example, we demonstrate the proposed idea of explaining the ROC curve, and visualising the uncertainties in these curves. For imbalanced datasets, the use of Precision-Recall Curve (PRC) is considered more appropriate, therefore we also demonstrate how to explain the PRCs with the help of Shapley values. The explanation of robustness can help analysts in a number of ways, for example, it can help in feature selection by identifying the irrelevant features that can be removed to reduce the computational complexity. It can also help in identifying the features having critical contributions or negative contributions towards robustness.
Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. 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. We introduce a less restrictive framework, Asymmetric Shapley values (ASVs), which are…
Shapley-Value-Based Graph Sparsification for GNN Inference
Department of Intelligent Systems Engineering Indiana University Bloomington Bloomington Indiana USA；Department of Computer Science \& Engineering Texas A\&M University College Station Texas USA；Indiana University Bloomington；Texas A\&M University
School of Mathematics and Physics, The University of Queensland（昆士兰大学数学与物理学院）；SimulaMet, Simula Research Laboratory（SimulaMet、Simula研究院）；Department of Mathematics and Statistics, La Trobe University（拉筹伯大学数学与统计学院）
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.…
For feature selection and related problems, we introduce the notion of classification game, a cooperative game, with features as players and hinge loss based characteristic function and relate a feature's contribution to Shapley value based error apportioning (SVEA) of total training error. Our major contribution is ($\star$) to show that for any dataset the threshold 0 on SVEA value identifies feature subset whose joint interactions for label prediction is significant or those features that span a subspace where the data is predominantly lying. In addition, our scheme ($\star$) identifies the…
Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration
Ludwig-Maximilians-Universität (LMU) Munich（慕尼黑大学）；John A. Paulson Harvard School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·保尔森工程与应用科学学院）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Wyss Institute for Biologically Inspired Engineering, Harvard University（哈佛大学怀斯生物启发工程研究所）
Texas A&M University（德克萨斯农工大学）；University of Science and Technology of China（中国科学技术大学）；West China Hospital（华西医院）
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree …
Institute for Health Informatics（健康信息学研究所）；Department of Medicine（医学系）；University of Minnesota（明尼苏达大学）
Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of using it as a model interpretation tool is yet to be described. In the current paper, we analyzed Shapley value in the Bayesian network framework. We established the relationship between Shapley value and conditional independence, a key concept in both predictive and causal modeling. Our results indicate that, eliminating a variable with high Shapley value from…
École Polytechnique, Institut Polytechnique de Paris（巴黎理工学院综合理工学院）；Société Générale（法国兴业银行）
In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions to the decision making are one of the most popular approaches to explain local individual and global predictions. By considering each output separately in multi-output tasks, these methods fail to provide complete feature explanations. We propose Shapley Chains to overcome this issue by including label interdependencies in the explanation design process. Shapley Chains assign Shaple…
University of Toulouse（图卢兹大学）；IRIT（图卢兹计算机科学研究所）；CNRS（法国国家科学研究中心）
This paper develops a rigorous argument for why the use of Shapley values in explainable AI (XAI) will necessarily yield provably misleading information about the relative importance of features for predictions. Concretely, this paper demonstrates that there exist classifiers, and associated predictions, for which the relative importance of features determined by the Shapley values will incorrectly assign more importance to features that are provably irrelevant for the prediction, and less importance to features that are provably relevant for the prediction. The paper also argues that, given r…
What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high per…
Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different features used as input to the model. Being based on solid game-theoretic principles, Shapley values uniquely satisfy several desirable properties, which is why they are increasingly used to explain the predictions of possibly complex and highly non-linear machine learning models. Shapley values are well calibrated to a user's intuition when features are indep…
Explainability in AI is crucial for model development, compliance with regulation, and providing operational nuance to predictions. The Shapley framework for explainability attributes a model's predictions to its input features in a mathematically principled and model-agnostic way. However, general implementations of Shapley explainability make an untenable assumption: that the model's features are uncorrelated. In this work, we demonstrate unambiguous drawbacks of this assumption and develop two solutions to Shapley explainability that respect the data manifold. One solution, based on generat…
University of Virginia（弗吉尼亚大学）；University of Chicago（芝加哥大学）
Data valuation, or the valuation of individual datum contributions, has seen growing interest in machine learning due to its demonstrable efficacy for tasks such as noisy label detection. In particular, due to the desirable axiomatic properties, several Shapley value approximation methods have been proposed. In these methods, the value function is typically defined as the predictive accuracy over the entire development set. However, this limits the ability to differentiate between training instances that are helpful or harmful to their own classes. Intuitively, instances that harm their own cl…
We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by changing some predictor values with others held fixed, potentially creating unlikely or even logically impossible combinations. Our cohort Shapley measure uses only observed data points. Instead of changing the value of a predictor we include or exclude subjects similar to the target subject on that predictor to form a similarity cohort. Then we apply Shapl…
Because of their strong theoretical properties, Shapley values have become very popular as a way to explain predictions made by black box models. Unfortuately, most existing techniques to compute Shapley values are computationally very expensive. We propose PDD-SHAP, an algorithm that uses an ANOVA-based functional decomposition model to approximate the black-box model being explained. This allows us to calculate Shapley values orders of magnitude faster than existing methods for large datasets, significantly reducing the amortized cost of computing Shapley values when many predictions need to…
Medical AI algorithms can often experience degraded performance when evaluated on previously unseen sites. Addressing cross-site performance disparities is key to ensuring that AI is equitable and effective when deployed on diverse patient populations. Multi-site evaluations are key to diagnosing such disparities as they can test algorithms across a broader range of potential biases such as patient demographics, equipment types, and technical parameters. However, such tests do not explain why the model performs worse. Our framework provides a method for quantifying the marginal and cumulative …
Université Paris-Saclay（巴黎萨克雷大学）；Ubisoft（育碧）；University of Granada（格拉纳达大学）
While Explainable Artificial Intelligence (XAI) is increasingly expanding more areas of application, little has been applied to make deep Reinforcement Learning (RL) more comprehensible. As RL becomes ubiquitous and used in critical and general public applications, it is essential to develop methods that make it better understood and more interpretable. This study proposes a novel approach to explain cooperative strategies in multiagent RL using Shapley values, a game theory concept used in XAI that successfully explains the rationale behind decisions taken by Machine Learning algorithms. Thro…
Center for Advanced Intelligence Project RIKEN（理化学研究所先进智能项目中心）
We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCA-based anomaly detection is applied, care must be taken in computing a value function for the Shapley values. We utilize the probabilistic view of PCA, particularly its conditional distribution, to exactly compute a value function for the Shapely values. We also present numerical examples, which imply that the Shapley values are advantageous for …
University of Tübingen（图宾根大学）；Tübingen AI Center（图宾根人工智能中心）
In explainable machine learning, local post-hoc explanation algorithms and inherently interpretable models are often seen as competing approaches. This work offers a partial reconciliation between the two by establishing a correspondence between Shapley Values and Generalized Additive Models (GAMs). We introduce $n$-Shapley Values, a parametric family of local post-hoc explanation algorithms that explain individual predictions with interaction terms up to order $n$. By varying the parameter $n$, we obtain a sequence of explanations that covers the entire range from Shapley Values up to a uniqu…
The University of Queensland（昆士兰大学）；Simula Research Laboratory（西穆拉研究实验室）；La Trobe University（拉筹伯大学）
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 number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game theory. While existing papers focus on the axiomatic motivation of Shapley values, and efficient techniques for computing them, they offer little justification for the game formulations used, and do not address the uncertainty implicit in their methods' outputs. For instance, the popular SHAP algorithm's formulation may give substantial attributions to featur…
ETH Zurich（苏黎世联邦理工学院）；Disney Research Zurich（苏黎世迪士尼研究中心）
The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about their reliability. On the other hand, the literature on cooperative game theory suggests Shapley values as a unique way of assigning relevance scores such that certain desirable properties are satisfied. Unfortunately, the exact evaluation of Shapley values is prohibitively expensive, exponential in the number of input features. In this work, by leveraging recen…
University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Local feature attribution methods are increasingly used to explain complex machine learning models. However, current methods are limited because they are extremely expensive to compute or are not capable of explaining a distributed series of models where each model is owned by a separate institution. The latter is particularly important because it often arises in finance where explanations are mandated. Here, we present DeepSHAP, a tractable method to propagate local feature attributions through complex series of models based on a connection to the Shapley value. We evaluate DeepSHAP across bi…
Shapley meets Rawls: an integrated framework for measuring and explaining unfairness
UM6P Airess University Mohammed VI Polytechnic（穆罕默德六世理工大学UM6P Airess大学）；Univ. Nîmes Chrome Um6p, Airess（尼姆大学Chrome实验室，穆罕默德六世理工大学Airess）；Liser Luxembourg（卢森堡社会经济研究所）
University of Oslo（奥斯陆大学）；Norwegian Computing Center（挪威计算中心）
Shapley values are today extensively used as a model-agnostic explanation framework to explain complex predictive machine learning models. Shapley values have desirable theoretical properties and a sound mathematical foundation in the field of cooperative game theory. Precise Shapley value estimates for dependent data rely on accurate modeling of the dependencies between all feature combinations. In this paper, we use a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously. We demonstrate through comprehensive simulation studies that our V…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values is a game theoretic concept that can be used for this purpose. The Shapley value framework has a series of desirable theoretical properties, and can in principle handle any predictive model. Kernel SHAP is a computationally efficient approximation to Shapley values in higher dimensions. Like several other existing methods, this approach assumes that the fea…
Paul G. Allen School of CSE（保罗·G·艾伦计算机科学与工程学院）；University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
In healthcare, making the best possible predictions with complex models (e.g., neural networks, ensembles/stacks of different models) can impact patient welfare. In order to make these complex models explainable, we present DeepSHAP for mixed model types, a framework for layer wise propagation of Shapley values that builds upon DeepLIFT (an existing approach for explaining neural networks). We show that in addition to being able to explain neural networks, this new framework naturally enables attributions for stacks of mixed models (e.g., neural network feature extractor into a tree model) as …
We introduce a new Shapley value approach for global sensitivity analysis and machine learning explainability. The method is based on the first-order partial derivatives of the underlying function. The computational complexity of the method is linear in dimension (number of features), as opposed to the exponential complexity of other Shapley value approaches in the literature. Examples from global sensitivity analysis and machine learning are used to compare the method numerically with activity scores, SHAP, and KernelSHAP.
University of Utah（犹他大学）；University of Arizona（亚利桑那大学）；Haverford College（哈弗福德学院）
Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game's unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily…
It is becoming increasingly important to explain complex, black-box machine learning models. Although there is an expanding literature on this topic, Shapley values stand out as a sound method to explain predictions from any type of machine learning model. The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. This methodology was then extended to explain dependent features with an underlying continuous distribution. In this paper, we propose a method to explain mixed (i.e. continuous, discrete, ordinal…
Predictions are the currency of a machine learning model, and to understand the model's behavior over segments of a dataset, or over time, is an important problem in machine learning research and practice. There currently is no systematic framework to understand this drift in prediction distributions over time or between two semantically meaningful slices of data, in terms of the input features and points. We propose GroupShapley and GroupIG (Integrated Gradients), as axiomatically justified methods to tackle this problem. In doing so, we re-frame all current feature/data importance measures b…
University Of California, San Diego（加州大学圣地亚哥分校）；Stanford University（斯坦福大学）
With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations of their underlying decision making processes by virtue of having a small number of discrete features. However, applying these methods to high-dimensional inputs such as images is not a trivial task. Images are composed of pixels at an atomic level and do not carry any interpretability by themselves. In this work, we seek to use annotated high-level interpr…
Explaining the predictions of opaque machine learning algorithms is an important and challenging task, especially as complex models are increasingly used to assist in high-stakes decisions such as those arising in healthcare and finance. Most popular tools for post-hoc explainable artificial intelligence (XAI) are either insensitive to context (e.g., feature attributions) or difficult to summarize (e.g., counterfactuals). In this paper, I introduce $\textit{rational Shapley values}$, a novel XAI method that synthesizes and extends these seemingly incompatible approaches in a rigorous, flexible…
