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 a model do not necessarily impair predictive performance, whereas eliminating a variable with low Shapley value from a model could impair performance. Therefore, using Shapley value for feature selection do not result in the most parsimonious and predictively optimal model in the general case. More importantly, Shapley value of a variable do not reflect their causal relationship with the target of interest.
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…
Feature selection is a crucial step in developing robust and powerful machine learning models. Feature selection techniques can be divided into two categories: filter and wrapper methods. While wrapper methods commonly result in strong predictive performances, they suffer from a large computational complexity and therefore take a significant amount of time to complete, especially when dealing with high-dimensional feature sets. Alternatively, filter methods are considerably faster, but suffer from several other disadvantages, such as (i) requiring a threshold value, (ii) not taking into accoun…
GRASP: group-Shapley feature selection for patients
1 Chinese Academy of Medical Sciences \& Peking Union Medical College, Beijing, China 2 Queen's University, Belfast, United Kingdom. 3 Heidelberg University, Heidelberg, Germany. Email
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…
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…
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…
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…
Norwegian University of Science and Technology (NTNU)（挪威科技大学 (NTNU)）
We investigate the effect of including domain knowledge about a robotic system's causal relations when generating explanations. To this end, we compare two methods from explainable artificial intelligence, the popular KernelSHAP and the recent causal SHAP, on a deep neural network trained using deep reinforcement learning on the task of controlling a lever using a robotic manipulator. A primary disadvantage of KernelSHAP is that its explanations represent only the features' direct effects on a model's output, not considering the indirect effects a feature can have on the output by affecting ot…
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 …
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）
Root causal analysis seeks to identify the set of initial perturbations that induce an unwanted outcome. In prior work, we defined sample-specific root causes of disease using exogenous error terms that predict a diagnosis in a structural equation model. We rigorously quantified predictivity using Shapley values. However, the associated algorithms for inferring root causes assume no latent confounding. We relax this assumption by permitting confounding among the predictors. We then introduce a corresponding procedure called Extract Errors with Latents (EEL) for recovering the error terms up to…
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…
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）
We describe a formal approach to identify 'root causes' of outliers observed in $n$ variables $X_1,\dots,X_n$ in a scenario where the causal relation between the variables is a known directed acyclic graph (DAG). To this end, we first introduce a systematic way to define outlier scores. Further, we introduce the concept of 'conditional outlier score' which measures whether a value of some variable is unexpected *given the value of its parents* in the DAG, if one were to assume that the causal structure and the corresponding conditional distributions are also valid for the anomaly. Finally, we …
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…
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.
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…
With the increasing adoption of predictive models trained using machine learning across a wide range of high-stakes applications, e.g., health care, security, criminal justice, finance, and education, there is a growing need for effective techniques for explaining such models and their predictions. We aim to address this problem in settings where the predictive model is a black box; That is, we can only observe the response of the model to various inputs, but have no knowledge about the internal structure of the predictive model, its parameters, the objective function, and the algorithm used t…
Microsoft Research（微软研究院）；Microsoft Bing Ads（微软必应广告）
Given an unexpected change in the output metric of a large-scale system, it is important to answer why the change occurred: which inputs caused the change in metric? A key component of such an attribution question is estimating the counterfactual: the (hypothetical) change in the system metric due to a specified change in a single input. However, due to inherent stochasticity and complex interactions between parts of the system, it is difficult to model an output metric directly. We utilize the computational structure of a system to break up the modelling task into sub-parts, such that each su…
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）
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
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）
Mathematical Sciences Department, Claremont McKenna College（克莱门特麦肯纳学院数学科学系）；Barcelona Supercomputing Center, Barcelona, Spain（巴塞罗那超级计算中心）；Department of Computer Science and Engineering, New York University（纽约大学计算机科学与工程系）
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…
ETH Zürich（苏黎世联邦理工学院）；MPI Tübingen（蒂宾根马克斯·普朗克研究所）；University of Copenhagen（哥本哈根大学）
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits …
