Enhancing the explainability of regression-based polynomial chaos expansion by Shapley additive explanations

• Published in: Reliability engineering & system safety 2023-04, Vol.232, p.109045, Article 109045
• Main Authors: Palar, Pramudita Satria, Zuhal, Lavi Rizki, Shimoyama, Koji
• Format: Article
• Language: English
• Subjects: Explainability; Polynomial chaos expansion; Shapley additive explanations
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2022.109045

Surrogate models are indispensable tools in uncertainty quantification and global sensitivity analysis. Polynomial chaos expansion (PCE) is one of the most widely used surrogate models, thanks to its faster convergence rate compared to Monte Carlo simulation. In some cases, especially for complex problems, analyzing the complexity of the random input–output relationship (e.g., nonlinearity and interactions between input variables) may reveal additional information and useful insight. To that end, this paper introduces the use of Shapley additive explanations (SHAP) to help the explanation of a PCE model. Originating from game theory and machine learning, SHAP computes the contribution of the input variables to the single prediction level. SHAP enables visual inspection of the nonlinearity and interaction between variables from a PCE model. In addition, as an alternative to Sobol indices, SHAP also quantifies the relative importance of the inputs to the output. This paper introduces a procedure to calculate SHAP values from a PCE model without explicitly building multiple PCE models. A fast and exact algorithm that enables the calculation of SHAP for high-dimensional problems is presented. The usefulness of SHAP with PCE is demonstrated on several algebraic and non-algebraic problems. •An explainable AI technique is implemented within polynomial chaos expansion (PCE).•The Shapley Additive Explanations (SHAP) enhances the explainability of PCE.•A method to analytically calculate SHAP for PCE is presented.•SHAP allows visualization of nonlinearity and interactions from the PCE model.•The method is demonstrated on three nonlinear uncertainty quantification problems.