Abstract
A method for the local and global uncertainty explanations of machine learning survival models by censored data in the framework of survival analysis is proposed. The method aims to select features of an object, which significantly impact on uncertainty of a survival model prediction corresponding to the object. The survival model is viewed as the black box, that is, only the input and the corresponding output are known. The first basic idea behind the method is to approximate the prediction uncertainty by the prediction uncertainty of the extended semi-parametric Cox proportional hazards model using the well-known generalized additive model. The second idea is to apply the neural additive model for getting the Cox approximation and to train the network in accordance with a specific loss function that takes into account the peculiarities of survival models. Results of the uncertainty explanation are represented in the form of shape functions which show the impact or contribution of every feature on the prediction provided by the black-box model. An algorithm implementing the method is presented. Numerical examples illustrate the proposed method by using real datasets including the German Breast Cancer Study Group 2 dataset and the Monoclonal Gammopathy dataset.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Hosmer, D., Lemeshow, S., May, S.: Applied Survival Analysis: Regression Modeling of Time to Event Data. Wiley, New Jersey (2008)
Wang, P., Li, Y., Reddy, C.: Machine learning for survival analysis: a survey. ACM Comput. Surv. (CSUR) 51, 1–36 (2019)
Ibrahim, N., Kudus, A., Daud, I., Bakar, M.A.: Decision tree for competing risks survival probability in breast cancer study. Int. J. Biol. Med. Res. 3, 25–29 (2008)
Nasejje, J., Mwambi, H., Dheda, K., Lesosky, M.: A comparison of the conditional inference survival forest model to random survival forests based on a simulation study as well as on two applications with time-to-event data. BMC Med. Res. Methodol. 17, 1–17 (2017)
Wright, M., Dankowski, T., Ziegler, A.: Unbiased split variable selection for random survival forests using maximally selected rank statistics. Stat. Med. 36, 1272–1284 (2017)
Belle, V.V., Pelckmans, K., Huffel, S.V., Suykens, J.: Support vector methods for survival analysis: a comparison between ranking and regression approaches. Artif. Intell. Med. 53, 107–118 (2011)
Faraggi, D., Simon, R.: A neural network model for survival data. Stat. Med. 14, 73–82 (1995)
Katzman, J., Shaham, U., Cloninger, A., Bates, J., Jiang, T., Kluger, Y.: Deepsurv: personalized treatment recommender system using a Cox proportional hazards deep neural network. BMC Med. Res. Methodol. 18, 1–12 (2018)
Arya, V., Bellamy, R., Chen, P.Y., Dhurandhar, A., Hind, M., Hoffman, S., Houde, S., Liao, Q., Luss, R., Mojsilovic, A., Mourad, S., Pedemonte, P., Raghavendra, R., Richards, J., Sattigeri, P., Shanmugam, K., Singh, M., Varshney, K., Wei, D., Zhang, Y.: One explanation does not fit all: a toolkit and taxonomy of AI explainability techniques. arXiv:1909.03012 (2019)
Guidotti, R., Monreale, A., Ruggieri, S., Turini, F., Giannotti, F., Pedreschi, D.: A survey of methods for explaining black box models. ACM Comput. Surv. 51, 93 (2019)
Molnar, C.: Interpretable Machine Learning: A Guide for Making Black Box Models Explainable. (2019). Published online, https://christophm.github.io/interpretable-ml-book/
Murdoch, W., Singh, C., Kumbier, K., Abbasi-Asl, R., Yua, B.: Interpretable machine learning: definitions, methods, and applications. arXiv:1901.04592 (2019)
Ribeiro, M., Singh, S., Guestrin, C.: “Why should I trust You?” Explaining the predictions of any classifier. arXiv:1602.04938v3 (2016)
Garreau, D., von Luxburg, U.: Explaining the explainer: a first theoretical analysis of LIME. arXiv:2001.03447 (2020)
Garreau, D., von Luxburg, U.: Looking deeper into tabular LIME. arXiv:2008.11092 (2020)
Kovalev, M., Utkin, L., Kasimov, E.: SurvLIME: A method for explaining machine learning survival models. Knowl. Based Syst. 203, 106164 (2020)
Kovalev, M., Utkin, L.: A robust algorithm for explaining unreliable machine learning survival models using the Kolmogorov-Smirnov bounds. Neural Netw. 132, 1–18 (2020)
Kovalev, M., Utkin, L.: Counterfactual explanation of machine learning survival models. arXiv:2006.16793 (2020)
Antoran, J., Bhatt, U., Adel, T., Weller, A., Hernandez-Lobato, J.: Getting a CLUE: A method for explaining uncertainty estimates. arXiv:2006.06848 (2020)
Depeweg, S., Hernandez-Lobato, J., Udluft, S., Runkler, T.: Sensitivity analysis for predictive uncertainty in Bayesian neural networks. arXiv:1712.03605 (2017)
Agarwal, R., Frosst, N., Zhang, X., Caruana, R., Hinton, G.: Neural additive models: Interpretable machine learning with neural nets. arXiv:2004.13912 (2020)
Hastie, T., Tibshirani, R.: Generalized additive models. Vol. 43. CRC Press (1990)
Cox, D.: Regression models and life-tables. J. Royal Statist. Soc. Series B (Methodological) 34, 187–220 (1972)
Utkin, L., Satyukov, E., Konstantinov, A.: SurvNAM: The machine learning survival model explanation. arXiv:2104.08903 (2021)
Konstantinov, A.V., Utkin, L.V.: A generalized stacking for implementing ensembles of gradient boosting machines. In: Cyber-Physical Systems: Digital Technologies and Applications. Springer International Publishing Series Title Studies in Systems, Decision and Control. Series Vol. 350. pp. 3–16. (2020). https://doi.org/10.1007/978-3-030-67892-0_1
Bolshakov, A.A., Veshneva, I.V., Lushin, D.: Mathematical model of integration of cyber-physical systems for solving problems of increasing the competitiveness of the regions In: Studies in Systems, Decision and Control. Society 5.0: Cyberspace for Advanced Human-Centered Society. Springer Nature Switzerland. Vol. 333. pp. 129–139 (2021). Decision and Control 333, https://doi.org/10.1007/978-3-030-63563-3_11. ISSN 2198-4182
Acknowledgements
This work is supported by the Russian Science Foundation under grant 21-11-00116.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Utkin, L., Konstantinov, A. (2022). An Extension of the Neural Additive Model for Uncertainty Explanation of Machine Learning Survival Models. In: Kravets, A.G., Bolshakov, A.A., Shcherbakov, M. (eds) Cyber-Physical Systems: Intelligent Models and Algorithms. Studies in Systems, Decision and Control, vol 417. Springer, Cham. https://doi.org/10.1007/978-3-030-95116-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-95116-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-95115-3
Online ISBN: 978-3-030-95116-0
eBook Packages: EngineeringEngineering (R0)