Shapley values are extensively used in explainable artificial intelligence (XAI) as a framework to explain predictions made by complex machine learning (ML) models. In this work, we focus on conditional Shapley values for predictive models fitted to tabular data and explain the prediction $f(\boldsymbol{x}^{*})$ for a single observation $\boldsymbol{x}^{*}$ at the time. Numerous Shapley value estimation methods have been proposed and empirically compared on an average basis in the XAI literature. However, less focus has been devoted to analyzing the precision of the Shapley value explanations on an individual basis. We extend our work in Olsen et al. (2023) by demonstrating and discussing that the explanations are systematically less precise for observations on the outer region of the training data distribution for all used estimation methods. This is expected from a statistical point of view, but to the best of our knowledge, it has not been systematically addressed in the Shapley value literature. This is crucial knowledge for Shapley values practitioners, who should be more careful in applying these observations' corresponding Shapley value explanations.
Shapley value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between the distribution of a feature and its Shapley value. We extend our analysis by discussing the difference that arises in Shapley explanation for different predicted outcomes from the same model. Our assessment is that Shapley value for particular feature not only depends on its expected mean but on other moments as well such as variance and there are disagreem…
There are many different methods in the literature for local explanation of machine learning results. However, the methods differ in their approaches and often do not provide same explanations. In this paper, we consider two recent methods: Integrated Gradients (Sundararajan, Taly, & Yan, 2017) and Baseline Shapley (Sundararajan and Najmi, 2020). The original authors have already studied the axiomatic properties of the two methods and provided some comparisons. Our work provides some additional insights on their comparative behavior for tabular data. We discuss common situations where the two …
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…
Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably due to its unique theoretical properties. The main drawback with Shapley values, however, is that its computational complexity grows exponentially in the number of input features, making it unfeasible in many real world situations where there could be hundreds or thousands of features. Furthermore, with many (dependent) features, presenting/visualizing and …
Kumamoto University（熊本大学）；Kurume University（久留米大学）；Saiseikai Kumamoto Hospital（济生会熊本医院）；Kyushu University Hospital（九州大学医院）
When using machine learning techniques in decision-making processes, the interpretability of the models is important. In the present paper, we adopted the Shapley additive explanation (SHAP), which is based on fair profit allocation among many stakeholders depending on their contribution, for interpreting a gradient-boosting decision tree model using hospital data. For better interpretability, we propose two novel techniques as follows: (1) a new metric of feature importance using SHAP and (2) a technique termed feature packing, which packs multiple similar features into one grouped feature to…
University of Oxford（牛津大学）；Amazon Research（亚马逊研究院）
Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently, explanations obtained are sensitive to model behaviour outside the data distribution, which may be irrelevant for all practical purposes. While on-manifold methods have been proposed which do not suffer from this problem, we show that such methods are overly dependent on the input data distribution, and therefore result in unintuitive and misleading explana…
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…
Complex models are commonly used in predictive modeling. In this paper we present R packages that can be used to explain predictions from complex black box models and attribute parts of these predictions to input features. We introduce two new approaches and corresponding packages for such attribution, namely live and breakDown. We also compare their results with existing implementations of state of the art solutions, namely lime that implements Locally Interpretable Model-agnostic Explanations and ShapleyR that implements Shapley values.
University of Oxford（牛津大学）；The London School of Hygiene & Tropical Medicine（伦敦卫生与热带医学院）；The Alan Turing Institute（艾伦·图灵研究所）
Shapley values provide model agnostic feature attributions for model outcome at a particular instance by simulating feature absence under a global population distribution. The use of a global population can lead to potentially misleading results when local model behaviour is of interest. Hence we consider the formulation of neighbourhood reference distributions that improve the local interpretability of Shapley values. By doing so, we find that the Nadaraya-Watson estimator, a well-studied kernel regressor, can be expressed as a self-normalised importance sampling estimator. Empirically, we ob…
While preference modelling is becoming one of the pillars of machine learning, the problem of preference explanation remains challenging and underexplored. In this paper, we propose \textsc{Pref-SHAP}, a Shapley value-based model explanation framework for pairwise comparison data. We derive the appropriate value functions for preference models and further extend the framework to model and explain \emph{context specific} information, such as the surface type in a tennis game. To demonstrate the utility of \textsc{Pref-SHAP}, we apply our method to a variety of synthetic and real-world datasets …
Volda University College（沃尔达大学学院）；University of Oslo（奥斯陆大学）
This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the predictions are useful. The paper proposes a novel approach to quantify how different data-clusters of the training data affect a prediction. The quantification is based on Shapley values, a concept which originates from coalitional game theory, developed to fairly distribute the payout among a set of cooperating players. A player's Shapley value is a measure o…
While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For instance, we show that the popular practice that consists in summing the SV of dummy variables is false as it provides wrong estimates of all the SV in the model and implies spurious interpretations. Based on the identification of null and active coalitions, and a coalitional version of the SV, we provide a correct computation and inference of important variab…
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…
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…
DistShap: Scalable GNN Explanations with Distributed Shapley Values
Indiana University Bloomington Indiana, USA；Wake Forest University North Carolina, USA；Texas A\&M University Texas, USA；Indiana University Bloomington；Wake Forest University；Texas A\&M University
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…
Functional Decomposition and Shapley Interactions for Interpreting Survival Models
Leibniz Institute for Prevention Research（预防研究与流行病学研究所）；Faculty of Mathematics（数学系）；Computer Science, University of Bremen（计算机科学，不莱梅大学）；University of Warsaw（华沙大学）；Centre for Credible AI, Warsaw University of Technology（可信人工智能中心，华沙技术大学）；Bielefeld University（比勒菲尔德大学）
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence, there have recently been attempts of appropriately modelling/estimating the dependence between the features. Although the proposed methods clearly outperform the traditional approach assuming independence, they have their weaknesses. In this paper we propose two new approaches for modelling the dependence between the features. Both approaches are based on vine c…
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…
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…
Artificial Intelligence in Medical Imaging (AI-Med), Department of Child and Adolescent Psychiatry, Ludwig-Maximilians-Universität, Munich, Germany（慕尼黑路德维希-马克西米利安大学儿童与青少年精神病学系医学成像人工智能（AI-Med））
Deep Neural Networks (DNNs) have an enormous potential to learn from complex biomedical data. In particular, DNNs have been used to seamlessly fuse heterogeneous information from neuroanatomy, genetics, biomarkers, and neuropsychological tests for highly accurate Alzheimer's disease diagnosis. On the other hand, their black-box nature is still a barrier for the adoption of such a system in the clinic, where interpretability is absolutely essential. We propose Shapley Value Explanation of Heterogeneous Neural Networks (SVEHNN) for explaining the Alzheimer's diagnosis made by a DNN from the 3D p…
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Ensemble-based modifications of the well-known SHapley Additive exPlanations (SHAP) method for the local explanation of a black-box model are proposed. The modifications aim to simplify SHAP which is computationally expensive when there is a large number of features. The main idea behind the proposed modifications is to approximate SHAP by an ensemble of SHAPs with a smaller number of features. According to the first modification, called ER-SHAP, several features are randomly selected many times from the feature set, and Shapley values for the features are computed by means of "small" SHAPs. T…
When a financial institution declines an application for credit, an adverse action (AA) is said to occur. The applicant is then entitled to an explanation for the negative decision. This paper focuses on credit decisions based on a predictive model for probability of default and proposes a methodology for AA explanation. The problem involves identifying the important predictors responsible for the negative decision and is straightforward when the underlying model is additive. However, it becomes non-trivial even for linear models with interactions. We consider models with low-order interaction…
New York University（纽约大学）；University of Washington（华盛顿大学）
Shapley values are widely used to explain black-box models, but they are costly to calculate because they require many model evaluations. We introduce FastSHAP, a method for estimating Shapley values in a single forward pass using a learned explainer model. FastSHAP amortizes the cost of explaining many inputs via a learning approach inspired by the Shapley value's weighted least squares characterization, and it can be trained using standard stochastic gradient optimization. We compare FastSHAP to existing estimation approaches, revealing that it generates high-quality explanations with orders…
The Wharton School of Business, University of Pennsylvania（宾夕法尼亚大学沃顿商学院）；University of Pennsylvania（宾夕法尼亚大学）
Many important questions about a model cannot be answered just by explaining how much each feature contributes to its output. To answer a broader set of questions, we generalize a popular, mathematically well-grounded explanation technique, Shapley Additive Explanations (SHAP). Our new method - Generalized Shapley Additive Explanations (G-SHAP) - produces many additional types of explanations, including: 1) General classification explanations; Why is this sample more likely to belong to one class rather than another? 2) Intergroup differences; Why do our model's predictions differ between grou…
Raptor Financial Technologies（Raptor金融技术公司）；Birkbeck College University of London（伦敦大学伯克贝克学院）；University of Birmingham（伯明翰大学）；Tokyo, Japan（东京，日本）
The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and intuitions: joint Shapley values measure a set of features' average contribution to a model's prediction. We prove the uniqueness of joint Shapley values, for any order of explanation. Results for games show that joint Shapley values present different insights from existing interaction indices, which assess the effect of a feature within a set of features. The joint…
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.…
The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the idea of estimating Shapley values via linear regression to understand and improve upon this approach. By analyzing the original KernelSHAP alongside a newly proposed unbiased version, we develop techniques to detect its convergence and calculate uncertainty estimates. We also find that the original version incurs a negligible increase in bias in exchange for…
University of Michigan（密歇根大学）；Microsoft Research（微软研究院）
Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature importance. However, current approaches that assign credit to nodes in the causal graph fail to explain the entire graph. In light of these limitations, we propose Shapley Flow, a novel approach to interpreting machine learning models. It considers the entire causal graph, and assigns credit to \textit{edges} instead of treating nodes as the fundamental unit of cred…
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability distributions are imprecise and represented by sets of distributions. The first idea behind the imprecise SHAP is a new approach for computing the marginal contribution of a feature, which fulfils the important efficiency property of Shapley values. The second idea is an attempt to consider a general approach to calculating and reducing interval-valued Shapley …
