Abstract
Tree models have made an impressive progress during the past years, while an important problem is to understand how these models predict, in particular for critical applications such as finance and medicine. For this issue, most previous works measured the importance of individual features. In this work, we consider the interpretation of feature groups, which is more effective to capture intrinsic structures and correlations of multiple features. We propose the Baseline Group Shapley value (short for BGShapvalue) to calculate the importance of a feature group for tree models. We further develop a polynomial algorithm, BGShapTree, to deal with the sum of exponential terms in the BGShapvalue. The basic idea is to decompose the BGShapvalue into leaves’ weights and exploit the relationships between features and leaves. Based on this idea, we could greedily search salient feature groups with large BGShapvalues. Extensive experiments have validated the effectiveness of our approach, in comparison with state-of-the-art methods on the interpretation of tree models.
Similar content being viewed by others
References
Breiman L. Random forests. Machine Learning, 2001, 45(1): 5–32
Chen T, Guestrin C. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016, 785–794
Zhou Z H, Feng J. Deep forest: towards an alternative to deep neural networks. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence. 2017, 3553–3559
Ribeiro M T, Singh S, Guestrin C. “Why should I trust you?”: explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016, 1135–1144
Grath R M, Costabello L, Le Van C, Sweeney P, Kamiab F, Shen Z, Lecue F. Interpretable credit application predictions with counterfactual explanations. 2018, arXiv preprint arXiv: 1811.05245
Lundberg S M, Nair B, Vavilala M S, Horibe M, Eisses M J, Adams T, Liston D E, Low D K W, Newman S F, Kim J, Lee S I. Explainable machine-learning predictions for the prevention of hypoxaemia during surgery. Nature Biomedical Engineering, 2018, 2(10): 749–760
Tjoa E, Guan C. A survey on explainable artificial intelligence (XAI): toward medical XAI. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(11): 4793–4813
Zablocki É, Ben-Younes H, Pérez P, Cord M. Explainability of deep vision-based autonomous driving systems: review and challenges. International Journal of Computer Vision, 2022, 130(10): 2425–2452
Breiman L, Friedman J, Olshen R A, Stone C J. Classification and Regression Trees. New York: CRC Press, 1984
Strobl C, Boulesteix A L, Zeileis A, Hothorn T. Bias in random forest variable importance measures: illustrations, sources and a solution. BMC Bioinformatics, 2007, 8: 25
Louppe G, Wehenkel L, Sutera A, Geurts P. Understanding variable importances in forests of randomized trees. In: Proceedings of the 26th International Conference on Neural Information Processing Systems. 2013, 431–439
Saabas A. Interpreting random forests. See interpreting-random-forests/website, 2014
Kazemitabar S J, Amini A A, Bloniarz A, Talwalkar A. Variable importance using decision trees. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. 2017, 425–434
Li X, Wang Y, Basu S, Kumbier K, Yu B. A debiased MDI feature importance measure for random forests. In: Proceedings of the 33rd International Conference on Neural Information Processing Systems. 2019, 723
Shapley L S. A value for n-person games. In: Kuhn H W, Tucker A W, eds. Contributions to the Theory of Games. Princeton: Princeton University Press, 1953, 307–317
Lundberg S M, Erion G, Chen H, DeGrave A, Prutkin J M, Nair B, Katz R, Himmelfarb J, Bansal N, Lee S I. From local explanations to global understanding with explainable AI for trees. Nature Machine Intelligence, 2020, 2(1): 56–67
Athanasiou M, Sfrintzeri K, Zarkogianni K, Thanopoulou A C, Nikita K S. An explainable XGBoost–based approach towards assessing the risk of cardiovascular disease in patients with type 2 diabetes mellitus. In: Proceedings of the 20th IEEE International Conference on Bioinformatics and Bioengineering. 2020, 859–864
Feng D C, Wang W J, Mangalathu S, Taciroglu E. Interpretable XGBoost-SHAP machine-learning model for shear strength prediction of squat RC walls. Journal of Structural Engineering, 2021, 147(11): 04021173
Sutera A, Louppe G, Huynh-Thu V A, Wehenkel L, Geurts P. From global to local MDI variable importances for random forests and when they are Shapley values. In: Proceedings of the 35th Conference on Neural Information Processing Systems. 2021, 3533–3543
Amoukou S I, Salaün T, Brunel N J B. Accurate Shapley values for explaining tree-based models. In: Proceedings of the 25th International Conference on Artificial Intelligence and Statistics. 2022, 2448–2465
Sundararajan M, Najmi A. The many Shapley values for model explanation. In: Proceedings of the 37th International Conference on Machine Learning. 2020, 859
Lundberg S M, Lee S I. A unified approach to interpreting model predictions. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. 2017, 4768–4777
Marichal J L. The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making. Discrete Applied Mathematics, 2000, 107(1–3): 139–164
Flores R, Molina E, Tejada J. Evaluating groups with the generalized Shapley value. 4OR, 2019, 17(2): 141–172
Marichal J L, Kojadinovic I, Fujimoto K. Axiomatic characterizations of generalized values. Discrete Applied Mathematics, 2007, 155(1): 26–43
Sundararajan M, Taly A, Yan Q. Axiomatic attribution for deep networks. In: Proceedings of the 34th International Conference on Machine Learning. 2017, 3319–3328
Štrumbelj E, Kononenko I. Explaining prediction models and individual predictions with feature contributions. Knowledge and Information Systems, 2014, 41(3): 647–665
Datta A, Sen S, Zick Y. Algorithmic transparency via quantitative input influence: theory and experiments with learning systems. In: Proceedings of 2016 IEEE Symposium on Security and Privacy. 2016, 598–617
Díaz-Uriarte R, de Andrés S A. Gene selection and classification of microarray data using random forest. BMC Bioinformatics, 2006, 7: 3
Ishwaran H. Variable importance in binary regression trees and forests. Electronic Journal of Statistics, 2007, 1: 519–537
Archer K J, Kimes R V. Empirical characterization of random forest variable importance measures. Computational Statistics & Data Analysis, 2008, 52(4): 2249–2260
Strobl C, Boulesteix A L, Kneib T, Augustin T, Zeileis A. Conditional variable importance for random forests. BMC Bioinformatics, 2008, 9: 307
Auret L, Aldrich C. Empirical comparison of tree ensemble variable importance measures. Chemometrics and Intelligent Laboratory Systems, 2011, 105(2): 157–170
Louppe G. Understanding random forests: from theory to practice. 2014, arXiv preprint arXiv: 1407.7502
Nembrini S, König I R, Wright M N. The revival of the Gini importance?. Bioinformatics, 2018, 34(21): 3711–3718
Scornet E. Trees, forests, and impurity-based variable importance. 2020, arXiv preprint arXiv: 2001.04295
Sagi O, Rokach L. Explainable decision forest: transforming a decision forest into an interpretable tree. Information Fusion, 2020, 61: 124–138
Tan S, Soloviev M, Hooker G, Wells M T. Tree space prototypes: another look at making tree ensembles interpretable. In: Proceedings of 2020 ACM-IMS on Foundations of Data Science Conference. 2020, 23–34
Lucic A, Oosterhuis H, Haned H, de Rijke M. FOCUS: flexible optimizable counterfactual explanations for tree ensembles. In: Proceedings of the 36th AAAI Conference on Artificial Intelligence. 2022, 5313–5322
Parmentier A, Vidal T. Optimal counterfactual explanations in tree ensembles. In: Proceedings of the 38th International Conference on Machine Learning. 2021, 8422–8431
Dutta S, Long J, Mishra S, Tilli C, Magazzeni D. Robust counterfactual explanations for tree-based ensembles. In: Proceedings of the 39th International Conference on Machine Learning. 2022, 5742–5756
Ignatiev A. Towards trustable explainable AI. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence. 2020, 5154–5158
Izza Y, Ignatiev A, Marques-Silva J. On explaining decision trees. 2020, arXiv preprint arXiv: 2010.11034
Izza Y, Marques-Silva J. On explaining random forests with SAT. In: Proceedings of the 30th International Joint Conference on Artificial Intelligence. 2021, 2584–2591
Ignatiev A, Izza Y, Stuckey P J, Marques-Silva J. Using MaxSAT for efficient explanations of tree ensembles. In: Proceedings of the 36th AAAI Conference on Artificial Intelligence. 2022, 3776–3785
Agarwal A, Tan Y S, Ronen O, Singh C, Yu B. Hierarchical shrinkage: improving the accuracy and interpretability of tree-based models. In: Proceedings of the 39th International Conference on Machine Learning. 2022, 111–135
Yang J. Fast TreeSHAP: accelerating SHAP value computation for trees. 2021, arXiv preprint arXiv: 2109.09847
Grömping U. Estimators of relative importance in linear regression based on variance decomposition. The American Statistician, 2007, 61(2): 139–147
Sun Y, Sundararajan M. Axiomatic attribution for multilinear functions. In: Proceedings of the 12th ACM Conference on Electronic Commerce. 2011, 177–178
Aas K, Jullum M, Løland A. Explaining individual predictions when features are dependent: more accurate approximations to Shapley values. Artificial Intelligence, 2021, 298: 103502
Chau S L, Hu R, Gonzalez J, Sejdinovic D. RKHS-SHAP: Shapley values for kernel methods. In: Proceedings of the 36th International Conference on Neural Information Processing Systems. 2022, 13050–13063
Ancona M, Oztireli C, Gross M. Explaining deep neural networks with a polynomial time algorithm for Shapley value approximation. In: Proceedings of the 36th International Conference on Machine Learning. 2019, 272–281
Ghorbani A, Zou J. Neuron Shapley: discovering the responsible neurons. In: Proceedings of the 34th International Conference on Neural Information Processing Systems. 2020, 5922–5932
Bento J, Saleiro P, Cruz A F, Figueiredo M A T, Bizarro P. TimeSHAP: explaining recurrent models through sequence perturbations. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2021, 2565–2573
Wang G, Chuang Y N, Du M, Yang F, Zhou Q, Tripathi P, Cai X, Hu X. Accelerating Shapley explanation via contributive cooperator selection. In: Proceedings of the 39th International Conference on Machine Learning. 2022, 22576–22590
Chen L, Lou S, Zhang K, Huang J, Zhang Q. HarsanyiNet: computing accurate Shapley values in a single forward propagation. In: Proceedings of the 40th International Conference on Machine Learning. 2023, 4804–4825
Štrumbelj E, Kononenko I, Šikonja M R. Explaining instance classifications with interactions of subsets of feature values. Data & Knowledge Engineering, 2009, 68(10): 886–904
Owen A B. Sobol’ indices and Shapley value. SIAM/ASA Journal on Uncertainty Quantification, 2014, 2(1): 245–251
Owen A B, Prieur C. On Shapley value for measuring importance of dependent inputs. SIAM/ASA Journal on Uncertainty Quantification, 2017, 5(1): 986–1002
Frye C, Rowat C, Feige I. Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability. In: Proceedings of the 34th International Conference on Neural Information Processing Systems. 2020, 1229–1239
Heskes T, Sijben E, Bucur I G, Claassen T. Causal Shapley values: exploiting causal knowledge to explain individual predictions of complex models. In: Proceedings of the 34th International Conference on Neural Information Processing Systems. 2020, 4778–4789
Dhamdhere K, Agarwal A, Sundararajan M. The Shapley Taylor interaction index. In: Proceedings of the 37th International Conference on Machine Learning. 2020, 9259–9268
Covert I, Lee S I. Improving KernelSHAP: practical Shapley value estimation using linear regression. In: Proceedings of the 24th International Conference on Artificial Intelligence and Statistics. 2021, 3457–3465
Janizek J D, Sturmfels P, Lee S I. Explaining explanations: axiomatic feature interactions for deep networks. The Journal of Machine Learning Research, 2021, 22(1): 104
Wang J, Zhang Y, Gu Y, Kim T K. SHAQ: incorporating Shapley value theory into multi-agent Q-learning. In: Proceedings of the 36th Conference on Neural Information Processing Systems. 2022, 5941–5954
Beechey D, Smith T M S, Şimşek Ö. Explaining reinforcement learning with Shapley values. In: Proceedings of the 40th International Conference on Machine Learning. 2023, 2003–2014
Ren J, Zhang D, Wang Y, Chen L, Zhou Z, Chen Y, Cheng X, Wang X, Zhou M, Shi J, Zhang Q. Towards a unified game-theoretic view of adversarial perturbations and robustness. In: Proceedings of the 35th Conference on Neural Information Processing Systems. 2021, 3797–3810
Chau S L, Muandet K, Sejdinovic D. Explaining the uncertain: stochastic Shapley values for Gaussian process models. In: Proceedings of the 37th Conference on Neural Information Processing Systems. 2023, 50769–50795
Watson D S, O’Hara J, Tax N, Mudd R, Guy I. Explaining predictive uncertainty with information theoretic Shapley values. In: Proceedings of the 37th Conference on Neural Information Processing Systems. 2023, 7330–7350
Janzing D, Minorics L, Blöbaum P. Feature relevance quantification in explainable AI: a causal problem. In: Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics. 2020, 2907–2916
Kumar I E, Venkatasubramanian S, Scheidegger C, Friedler S A. Problems with Shapley-value-based explanations as feature importance measures. In: Proceedings of the 37th International Conference on Machine Learning. 2020, 5491–5500
Kumar I E, Scheidegger C, Venkatasubramanian S, Friedler S A. Shapley residuals: quantifying the limits of the Shapley value for explanations. In: Proceedings of the 35th Conference on Neural Information Processing Systems. 2021, 26598–26608
Kwon Y, Zou J. WeightedSHAP: analyzing and improving Shapley based feature attributions. In: Proceedings of the 36th Conference on Neural Information Processing Systems. 2022, 34363–34376
Van den Broeck G, Lykov A, Schleich M, Suciu D. On the tractability of SHAP explanations. In: Proceedings of the 35th AAAI Conference on Artificial Intelligence. 2021, 6505–6513
Bordt S, von Luxburg U. From Shapley values to generalized additive models and back. In: Proceedings of the 26th International Conference on Artificial Intelligence and Statistics. 2023, 709–745
Jullum M, Redelmeier A, Aas K. groupShapley: efficient prediction explanation with Shapley values for feature groups. 2021, arXiv preprint arXiv: 2106.12228
Miroshnikov A, Kotsiopoulos K, Filom K, Kannan A R. Stability theory of game-theoretic group feature explanations for machine learning models. 2021, arXiv preprint arXiv: 2102.10878
Au Q, Herbinger J, Stachl C, Bischl B, Casalicchio G. Grouped feature importance and combined features effect plot. Data Mining and Knowledge Discovery, 2022, 36(4): 1401–1450
Vanschoren J, van Rijn J N, Bischl B, Torgo L. OpenML: networked science in machine learning. ACM SIGKDD Explorations Newsletter, 2014, 15(2): 49–60
Kelly M, Longjohn R, Nottingham K. The UCI Machine Learning Repository. See archive.ics.uci.edu website. 2024
Samek W, Binder A, Montavon G, Lapuschkin S, Müller K R. Evaluating the visualization of what a deep neural network has learned. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(11): 2660–2673
Lundberg S M, Erion G G, Lee S I. Consistent individualized feature attribution for tree ensembles. 2018, arXiv preprint arXiv: 1802.03888
Acknowledgements
The authors want to thank the editors and reviewers for their helpful comments and suggestions. The authors also thank Jia-He Yao for helpful advice. This research was supported by the National Science and Technology Major Project (2021ZD0112802) and the National Natural Science Foundation of China (Grant No. 62376119).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests The authors declare that they have no competing interests or financial conflicts to disclose.
Additional information
Fan Xu received his BSc degree from Southeast University, China in 2020. Currently, he is working towards the PhD degree in Nanjing University, China. His research interest is mainly on machine learning.
Zhi-Jian Zhou received his BSc degree from Dalian University of Technology, China in 2021. He is now a graduate student in Nanjing University, China. His research interest is mainly on hypothesis testing.
Jie Ni received his BSc degree from Nanjing University, China in 2021. Currently, he is a graduate student in Nanjing University, China. His research interest include machine learning and data mining.
Wei Gao received his PhD degree from Nanjing University, China in 2014, and he is currently an associate professor of School of Artificial Intelligence in Nanjing University, China. His research interests include learning theory. His works have been published in top-tier international journals or conference proceedings such as AIJ, IEEE TPAMI, COLT, ICML and NeurIPS. He is also a co-author of the book Introduction to the Theory of Machine Learning.
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Xu, F., Zhou, ZJ., Ni, J. et al. Interpretation with baseline shapley value for feature groups on tree models. Front. Comput. Sci. 19, 195316 (2025). https://doi.org/10.1007/s11704-024-40117-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11704-024-40117-2