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, and categorical) dependent features by modeling the dependence structure of the features using conditional inference trees. We demonstrate our proposed method against the current industry standards in various simulation studies and find that our method often outperforms the other approaches. Finally, we apply our method to a real financial data set used in the 2018 FICO Explainable Machine Learning Challenge and show how our explanations compare to the FICO challenge Recognition Award winning team.
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…
Duke-NUS Medical School（杜克-新加坡国立大学医学院）；Singapore Health Services（新加坡保健服务集团）；National University of Singapore（新加坡国立大学）
Current practice in interpretable machine learning often focuses on explaining the final model trained from data, e.g., by using the Shapley additive explanations (SHAP) method. The recently developed Shapley variable importance cloud (ShapleyVIC) extends the current practice to a group of "nearly optimal models" to provide comprehensive and robust variable importance assessments, with estimated uncertainty intervals for a more complete understanding of variable contributions to predictions. ShapleyVIC was initially developed for applications with traditional regression models, and the benefit…
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…
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 …
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 …
Uncertainty-Aware Multimodal Learning via Conformal Shapley Intervals
Department of Statistics and Data Science, UCLA（统计与数据科学系， UCLA）；Merck & Co（默克公司）；Department of Biostatistics, UCLA（生物统计学系， UCLA）；Departments of Statistics and Data Science, and of Biostatistics, UCLA（统计与数据科学系以及生物统计学系， UCLA）
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…
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 …
Duke-NUS Medical School（杜克-新加坡国立大学医学院）；Singapore Health Services（新加坡保健服务集团）；Singapore General Hospital（新加坡中央医院）；National University of Singapore（新加坡国立大学）；Duke University（杜克大学）
Interpretable machine learning has been focusing on explaining final models that optimize performance. The current state-of-the-art is the Shapley additive explanations (SHAP) that locally explains variable impact on individual predictions, and it is recently extended for a global assessment across the dataset. Recently, Dong and Rudin proposed to extend the investigation to models from the same class as the final model that are "good enough", and identified a previous overclaim of variable importance based on a single model. However, this method does not directly integrate with existing Shapl…
A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty
Leibniz Institute for Prevention Research and Epidemiology – BIPS（莱布尼茨预防研究与流行病学研究所——BIPS）；University of Bremen（不来梅大学）；Simula Research Laboratory（西穆拉研究实验室）；Telenor Research & Innovation（挪威电信研究与创新部）；Norwegian Computing Center（挪威计算中心）
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…
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…
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…
Polytechnique Montréal（蒙特利尔工程学院）；Université de Laval à Québec（魁北克拉瓦尔大学）
Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the number of input features of an opaque model. Now, with efficient implementations such as Interventional TreeSHAP, this exponential burden is alleviated assuming one is explaining ensembles of decision trees. Although Interventional TreeSHAP has risen in popularity, it still lacks a formal proof of how/why it works. We provide such proof with the aim of not on…
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 …
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…
Shapley-related techniques have gained attention as both global and local interpretation tools because of their desirable properties. However, their computation using conditional expectations is computationally expensive. Approximation methods suggested in the literature have limitations. This paper proposes the use of a surrogate model-based tree to compute Shapley and SHAP values based on conditional expectation. Simulation studies show that the proposed algorithm provides improvements in accuracy, unifies global Shapley and SHAP interpretation, and the thresholding method provides a way to …
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 …
We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a broader variety of functions that arise from practical applications of ML in domains like financial services. GIG is constructed to overcome limitations of Shapley (1953) and Aumann-Shapley (1974), and has desirable properties when compared to other approaches. We prove GIG is the only correct method, under a small set of reasonable axioms, for providing ex…
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…
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）
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…
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 …
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…
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…
SINTEF DIGITAL（挪威科学与工业研究基金会数字研究所）；Norwegian University of Science and Technology（挪威科技大学）；SimulaMet（西穆拉代谢研究所）；Yale School of Public Health（耶鲁大学公共卫生学院）
Estimating feature importance is a significant aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a Shapley value based framework for inferring the importance of individual features, including uncertainty in the estimator. We build upon the recently published feature importance measure of SAGE (Shapley additive global importance) and introduce sub-SAGE which can be estimated without resampling for tree-based models. We argue that the uncertainties can be …
University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application depende…
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…
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
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…
We discuss promising recent contributions on quantifying feature relevance using Shapley values, where we observed some confusion on which probability distribution is the right one for dropped features. We argue that the confusion is based on not carefully distinguishing between observational and interventional conditional probabilities and try a clarification based on Pearl's seminal work on causality. We conclude that unconditional rather than conditional expectations provide the right notion of dropping features in contradiction to the theoretical justification of the software package SHAP.…
Auburn University（奥本大学）；DESY（德国电子同步加速器研究所）；Humboldt-Universität zu Berlin（柏林洪堡大学）；BASIS Independent Silicon Valley（贝赛思独立学校硅谷校区）；Stanford Online High School（斯坦福在线高中）；NTNU（挪威科技大学）；SimulaMet（SimulaMet研究所）
The analysis of causation is a challenging task that can be approached in various ways. With the increasing use of machine learning based models in computational socioeconomics, explaining these models while taking causal connections into account is a necessity. In this work, we advocate the use of an explanatory framework from cooperative game theory augmented with $do$ calculus, namely causal Shapley values. Using causal Shapley values, we analyze socioeconomic disparities that have a causal link to the spread of COVID-19 in the USA. We study several phases of the disease spread to show how …
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…
Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream machine learning task that is an important use case and popular benchmark for NE methods. Unfortunately, while NE methods perform exceedingly well at this task, they are lacking in transparency as compared to simpler LP approaches. We introduce ExplaiNE, an approach to offer cou…
