Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this paper, we derive the first analytic expressions for DShapley for the canonical problems of linear regression, binary classification, and non-parametric density estimation. These analytic forms provide new algorithms to estimate DShapley that are several orders of magnitude faster than previous state-of-the-art methods. Furthermore, our formulas are directly interpretable and provide quantitative insights into how the value varies for different types of data. We demonstrate the practical efficacy of our approach on multiple real and synthetic datasets.
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Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework -- distributional Shapley -- where the …
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 …
The coefficient of determination, the $R^2$, is often used to measure the variance explained by an affine combination of multiple explanatory covariates. An attribution of this explanatory contribution to each of the individual covariates is often sought in order to draw inference regarding the importance of each covariate with respect to the response phenomenon. A recent method for ascertaining such an attribution is via the game theoretic Shapley value decomposition of the coefficient of determination. Such a decomposition has the desirable efficiency, monotonicity, and equal treatment prope…
This paper studies a basic notion of distributional shape known as orthounimodality (OU) and its use in shape-constrained distributionally robust optimization (DRO). As a key motivation, we argue how such type of DRO is well-suited to tackle multivariate extreme event estimation by giving statistically valid confidence bounds on target extremal probabilities. In particular, we explain how DRO can be used as a nonparametric alternative to conventional extreme value theory that extrapolates tails based on theoretical limiting distributions, which could face challenges in bias-variance control an…
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 …
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）
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…
The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation algorithm called ``Group Testing-based SV estimator'' which achieves favorable asymptotic sample complexity. In this technical note, we present several improvements in the analysis and design choices of this SV estimator. Moreover, we point out that the Group Testing-based SV estimator does not fully reuse the collected samples. Our analysis and insights contribute…
Annotating the right set of data amongst all available data points is a key challenge in many machine learning applications. Batch active learning is a popular approach to address this, in which batches of unlabeled data points are selected for annotation, while an underlying learning algorithm gets subsequently updated. Increasingly larger batches are particularly appealing in settings where data can be annotated in parallel, and model training is computationally expensive. A key challenge here is scale - typical active learning methods rely on diversity techniques, which select a diverse set…
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）
A novel application of Shapley values for large multidimensional time-series data: Applying explainable AI to a DNA profile classification neural network
Adelaide Data Science Centre（阿德莱德数据科学中心）；University of Adelaide（阿德莱德大学）；Forensic Science SA（南澳大利亚法医科学中心）；College of Science and Engineering, Flinders University（弗林德斯大学科学与工程学院）
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…
Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian learning games where players perform a Bayesian inference using their combined data, and the posterior-prior KL divergence is used as the characteristic function. We show that for any two players, under some regularity conditions, their difference in Shapley value converges in probability to the difference in Shapley value of a limiting game whose characteristic…
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…
Nvidia Corporation（英伟达公司）；University of South Carolina（南卡罗来纳大学）；University of Waikato（怀卡托大学）
Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more sophisticated quasi-Monte Carlo methods have not yet been applied to the space of permutations. To addres…
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 …
Data Valuation by Fusing Global and Local Statistical Information
Peking University（北京大学）；University of Chinese Academy of Sciences（中国科学院大学）；Hong Kong Baptist University（香港 Baptist大学）；Renmin University of China（中国人民大学）
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）
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
