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Explainable Learning with Gaussian Processes (2403.07072v1)

Published 11 Mar 2024 in cs.LG and eess.SP

Abstract: The field of explainable artificial intelligence (XAI) attempts to develop methods that provide insight into how complicated machine learning methods make predictions. Many methods of explanation have focused on the concept of feature attribution, a decomposition of the model's prediction into individual contributions corresponding to each input feature. In this work, we explore the problem of feature attribution in the context of Gaussian process regression (GPR). We take a principled approach to defining attributions under model uncertainty, extending the existing literature. We show that although GPR is a highly flexible and non-parametric approach, we can derive interpretable, closed-form expressions for the feature attributions. When using integrated gradients as an attribution method, we show that the attributions of a GPR model also follow a Gaussian process distribution, which quantifies the uncertainty in attribution arising from uncertainty in the model. We demonstrate, both through theory and experimentation, the versatility and robustness of this approach. We also show that, when applicable, the exact expressions for GPR attributions are both more accurate and less computationally expensive than the approximations currently used in practice. The source code for this project is freely available under MIT license at https://github.com/KurtButler/2024_attributions_paper.

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References (62)
  1. Real estate valuation data set. UCI Machine Learning Repository, 2018. DOI: https://doi.org/10.24432/C5J30W.
  2. Sanity checks for saliency maps. Advances in neural information processing systems, 31, 2018.
  3. Random Fields and Geometry. Springer, 2007.
  4. Explainable artificial intelligence: an analytical review. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 11(5):e1424, 2021.
  5. Explainable artificial intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion, 58:82–115, 2020.
  6. Values of Non-Atomic Games. Princeton University Press, 2015.
  7. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLOS One, 10(7):e0130140, 2015.
  8. How to explain individual classification decisions. The Journal of Machine Learning Research, 11:1803–1831, 2010.
  9. Extracting training data from diffusion models. In 32nd USENIX Security Symposium (USENIX Security 23), pages 5253–5270, 2023.
  10. Explaining the uncertain: Stochastic Shapley values for Gaussian process models. arXiv preprint arXiv:2305.15167, 2023.
  11. Modeling wine preferences by data mining from physicochemical properties. Decis. Support Syst., 47:547–553, 2009a. URL https://api.semanticscholar.org/CorpusID:2996254.
  12. Wine Quality. UCI Machine Learning Repository, 2009b. DOI: https://doi.org/10.24432/C56S3T.
  13. Deep Gaussian processes. In Artificial Intelligence and Statistics, pages 207–215. PMLR, 2013.
  14. The perils and pitfalls of explainable AI: Strategies for explaining algorithmic decision-making. Government Information Quarterly, 39(2):101666, 2022.
  15. Additive Gaussian processes. Advances in Neural Information Processing Systems, 24, 2011.
  16. Three methods to share joint costs or surplus. Journal of Economic Theory, 87(2):275–312, 1999.
  17. Eric J Friedman. Paths and consistency in additive cost sharing. International Journal of Game Theory, 32:501–518, 2004.
  18. The false hope of current approaches to explainable artificial intelligence in health care. The Lancet Digital Health, 3(11):e745–e750, 2021.
  19. Mark N Gibbs. Bayesian Gaussian processes for regression and classification. PhD thesis, Citeseer, 1998.
  20. Deep sparse rectifier neural networks. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pages 315–323. JMLR Workshop and Conference Proceedings, 2011. URL http://proceedings.mlr.press/v15/glorot11a/glorot11a.pdf.
  21. Ulrike Grömping. Estimators of relative importance in linear regression based on variance decomposition. The American Statistician, 61(2):139–147, 2007.
  22. Michael T Heath. Scientific Computing: An Introductory Survey. SIAM, second edition, 2018.
  23. Gaussian processes for big data. In Uncertainty in Artificial Intelligence, page 282, 2013.
  24. Protoshotxai: Using prototypical few-shot architecture for explainable AI. Journal of Machine Learning Research, 24(325):1–49, 2023. URL http://jmlr.org/papers/v24/21-1261.html.
  25. Applications of physics-informed neural networks in power systems-a review. IEEE Transactions on Power Systems, 38(1):572–588, 2022.
  26. Explainable deep learning in healthcare: A methodological survey from an attribution view. WIREs Mechanisms of Disease, 14(3):e1548, 2022.
  27. ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, volume 25, 2012.
  28. Sparse spectrum Gaussian process regression. The Journal of Machine Learning Research, 11:1865–1881, 2010.
  29. Jean-François Le Gall. Brownian Motion, Martingales, and Stochastic Calculus, volume 274 of Graduate Texts in Mathematics. Springer, 2016.
  30. John M Lee. Introduction to Smooth Manifolds, volume 218 of Graduate Texts in Mathematics. Springer, 2012.
  31. A unified approach to interpreting model predictions. In Advances in Neural Information Processing Systems, volume 30, 2017. URL https://proceedings.neurips.cc/paper_files/paper/2017/file/8a20a8621978632d76c43dfd28b67767-Paper.pdf.
  32. A rigorous study of integrated gradients method and extensions to internal neuron attributions. In International Conference on Machine Learning, pages 14485–14508. PMLR, 2022.
  33. Sampling permutations for Shapley value estimation. The Journal of Machine Learning Research, 23(1):2082–2127, 2022.
  34. Kevin P. Murphy. Probabilistic Machine Learning: An Introduction. MIT Press, 2022. URL probml.ai.
  35. Radford M Neal. Bayesian Learning for Neural Networks, volume 118 of Lecture Notes in Statistics. Springer, 1996.
  36. XAI beyond classification: Interpretable neural clustering. The Journal of Machine Learning Research, 23(1):227–254, 2022.
  37. Gaussian Processes for Machine Learning. MIT Press, 2006. URL https://gaussianprocess.org/gpml/.
  38. Model-agnostic interpretability of machine learning. arXiv preprint arXiv:1606.05386, 2016.
  39. Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming. Statistics and Computing, 33(1):17, 2023.
  40. Explaining classifications for individual instances. IEEE Transactions on Knowledge and Data Engineering, 20(5):589–600, 2008.
  41. Cynthia Rudin. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5):206–215, 2019.
  42. Explaining deep neural networks and beyond: A review of methods and applications. Proceedings of the IEEE, 109(3):247–278, 2021.
  43. Sarem Seitz. Gradient-based explanations for Gaussian process regression and classification models. arXiv preprint arXiv:2205.12797, 2022.
  44. Lloyd S Shapley. A value for n-person games. Contributions to the Theory of Games, pages 307–317, 1953.
  45. Optimization methods for interpretable differentiable decision trees applied to reinforcement learning. In International conference on artificial intelligence and statistics, pages 1855–1865. PMLR, 2020.
  46. Deep inside convolutional networks: visualising image classification models and saliency maps. In Proceedings of the International Conference on Learning Representations (ICLR). ICLR, 2014.
  47. Derivative observations in Gaussian process models of dynamic systems. Advances in Neural Information Processing Systems, 15, 2002.
  48. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.
  49. Michael L Stein. Interpolation of Spatial Data: Some Theory for Kriging. Springer Science & Business Media, 1999.
  50. Explaining prediction models and individual predictions with feature contributions. Knowledge and Information Systems, 41(3):647–665, 2014.
  51. Explaining instance classifications with interactions of subsets of feature values. Data & Knowledge Engineering, 68(10):886–904, 2009.
  52. Visualizing the impact of feature attribution baselines. Distill, 5(1):e22, 2020. URL https://distill.pub/2020/attribution-baselines/.
  53. The many Shapley values for model explanation. In International Conference on Machine Learning, pages 9269–9278. PMLR, 2020.
  54. Axiomatic attribution for deep networks. In International Conference on Machine Learning, pages 3319–3328. PMLR, 2017.
  55. Evaluating XAI: A comparison of rule-based and example-based explanations. Artificial Intelligence, 291:103404, 2021.
  56. Analyzing multi-head self-attention: Specialized heads do the heavy lifting, the rest can be pruned. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. Association for Computational Linguistics, 2019.
  57. Grace Wahba. Spline Models for Observational Data. SIAM, 1990.
  58. Deep kernel learning. In Artificial Intelligence and Statistics, pages 370–378. PMLR, 2016.
  59. Breast Cancer Wisconsin (Prognostic). UCI Machine Learning Repository, 1995. DOI: https://doi.org/10.24432/C5GK50.
  60. GNNExplainer: Generating explanations for graph neural networks. Advances in Neural Information Processing Systems, 32, 2019.
  61. Gaussian process regression with interpretable sample-wise feature weights. IEEE Transactions on Neural Networks and Learning Systems, 2021.
  62. From black-box to white-box: Interpretable learning with kernel machines. In Machine Learning and Data Mining in Pattern Recognition: 14th International Conference, MLDM 2018, New York, NY, USA, July 15-19, 2018, Proceedings, Part I 14, pages 213–227. Springer, 2018.

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