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 of that player's contribution. Shapley values are often used to quantify feature importance, ie. how features affect a prediction. This paper extends this to cluster importance, letting clusters of the training data act as players in a game where the predictions are the payouts. The novel methodology proposed in this paper lets us explore and investigate how different clusters of the training data affect the predictions made by any black-box model, allowing new aspects of the reasoning and inner workings of a prediction model to be conveyed to the users. The methodology is fundamentally different from existing explanation methods, providing insight which would not be available otherwise, and should complement existing explanation methods, including explanations based on feature importance.
Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable …
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…
University of California, Berkeley（加州大学伯克利分校）；Georgia Institute of Technology（佐治亚理工学院）；Ant Financial（蚂蚁金服）；Voleon Group（Voleon集团）
We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score have been proposed as a fair way of computing feature attributions of this kind, but incur an exponential complexity in the number of features. This combinatorial explosion arises from the definition of the Shapley value and prevents these methods from being scalable to large data sets and complex models. We focus on settings in which the data have a graph …
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…
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…
Federated Learning is introduced to protect privacy by distributing training data into multiple parties. Each party trains its own model and a meta-model is constructed from the sub models. In this way the details of the data are not disclosed in between each party. In this paper we investigate the model interpretation methods for Federated Learning, specifically on the measurement of feature importance of vertical Federated Learning where feature space of the data is divided into two parties, namely host and guest. For host party to interpret a single prediction of vertical Federated Learning…
Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and neural networks, as they can efficiently handle dependence and interactions in the data, as opposed to most other variable importance measures. However, estimating Shapley effects is a challenging task, because of the computational complexity and the conditional expectation estimates. Accordingly, existing Shapley algorithms have flaws: a costly running time, or…
How important are the genes to explain the outcome - the asymmetric Shapley value as an honest importance metric for high-dimensional features
Dept of Epidemiology and Data Science, Amsterdam Public Health research institute, Amsterdam University Medical Centers（流行病学与数据科学系，阿姆斯特丹公共卫生研究所，阿姆斯特丹大学医学中心）；Norwegian Computing Center（挪威计算中心）
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data science and machine learning. However, the time complexity to compute Shapley values based on the original formula is exponential, and as the number of features increases, this becomes infeasible. Castro et al. [1] developed a sampling algorithm, to estimate Shapley values. In this work, we propose a new sampling method based on a multilinear extension techni…
There is much interest lately in explainability in statistics and machine learning. One aspect of explainability is to quantify the importance of various features (or covariates). Two popular methods for defining variable importance are LOCO (Leave Out COvariates) and Shapley Values. We take a look at the properties of these methods and their advantages and disadvantages. We are particularly interested in the effect of correlation between features which can obscure interpretability. Contrary to some claims, Shapley values do not eliminate feature correlation. We critique the game theoretic axi…
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…
Virginia Tech（弗吉尼亚理工大学）；UIUC（伊利诺伊大学厄巴纳-香槟分校）；Shanhai Jiaotong University（上海交通大学）；UC Irvine（加州大学尔湾分校）；ETH Zurich（苏黎世联邦理工学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；UC Berkeley（加州大学伯克利分校）
Quantifying the importance of each training point to a learning task is a fundamental problem in machine learning and the estimated importance scores have been leveraged to guide a range of data workflows such as data summarization and domain adaption. One simple idea is to use the leave-one-out error of each training point to indicate its importance. Recent work has also proposed to use the Shapley value, as it defines a unique value distribution scheme that satisfies a set of appealing properties. However, calculating Shapley values is often expensive, which limits its applicability in real-…
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）
Humboldt University of Berlin（柏林洪堡大学）；Singapore Management University（新加坡管理大学）；National Yang Ming Chiao Tung University（国立阳明交通大学）；Charles University（查理大学）；Institute for Digital Assets（数字资产研究院）
Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the importance of each feature in a model, at the row level. In other words, Shapley values represent the importance of a feature for a particular row, especially for Classification or Regression problems. One of the biggest limitations of Shapley vales is that, Shapley value calculations assume all the features are uncorrelated (independent of each other), this …
Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known COMPAS recidivism data as our example. This approach allows one to identify for each individual in a data set the extent to which they were adversely or beneficially affected by their value of a protected attribute such as their race. The method can do this even if race was not one of the original predictors and even if it does not have access to a proprietary…
ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation
Department of Statistics, LMU Munich（LMU慕尼黑统计系）；Institute for Informatics, LMU Munich（LMU慕尼黑信息学院）；Department of Computer Science, TU Dortmund University（图腾大学计算机科学系）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Lamarr Institute for Machine Learning（拉马尔机器学习研究所）
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.…
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…
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 …
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…
Emory University（埃默里大学）；Georgia Institute of Technology（佐治亚理工学院）
Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation based on their contribution to the models. Shapley value is the only value division scheme used for compensation allocation that meets three desirable criteria: group rationality, fairness, and additivity. In cooperative game theory, the marginal contribution of each contributor to each coalition is a nonnegative value. However, in machine learning model train…
This paper discusses an application of Shapley values in the causal inference field, specifically on how to select the top confounder variables for coarsened exact matching method in a scalable way. We use a dataset from an observational experiment involving LinkedIn members as a use case to test its applicability, and show that Shapley values are highly informational and can be leveraged for its robust importance-ranking capability.
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…
Department of Statistics, LMU Munich（LMU慕尼黑统计系）；Department of Electrical Engineering and Computer Science, UC Berkeley（伯克利电子工程与计算机科学系）；Mathematical Sciences Department, Claremont McKenna College（克莱门茨麦肯纳学院数学科学系）
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…
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）
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
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 …
In the institutional research mode, in order to explore which characteristics are the best indicators for predicting academic risk from the student behavior data sets that have high-dimensional, unbalanced classified small sample, it transforms the academic risk prediction of college students into a binary classification task. It predicts academic risk based on the LightGBM model and the interpretable machine learning method of Shapley value. The simulation results show that from the global perspective of the prediction model, characteristics such as the quality of academic partners, the seati…
Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals
Département de Mathématiques, Université du Québec à Montréal（魁北克大学蒙特利尔分校数学系）；Institut Intelligence et Données, Université Laval（拉瓦尔大学智能与数据研究所）；CNRS - Université de Montréal（法国国家科学研究中心-蒙特利尔大学）；CRM – CNRS Aix Marseille Univ, CNRS, AMSE, Marseille, France（法国国家科学研究中心-阿维尼昂大学）
Intel Labs（英特尔实验室）；Anticipatory Computing Lab（前瞻性计算实验室）；University of Pennsylvania（宾夕法尼亚大学）；Penn Center for Learning Analytics（宾夕法尼亚大学学习分析中心）
The development of real-time affect detection models often depends upon obtaining annotated data for supervised learning by employing human experts to label the student data. One open question in annotating affective data for affect detection is whether the labelers (i.e., human experts) need to be socio-culturally similar to the students being labeled, as this impacts the cost feasibility of obtaining the labels. In this study, we investigate the following research questions: For affective state annotation, how does the socio-cultural background of human expert labelers, compared to the subje…
