# Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations

arXiv: https://arxiv.org/abs/2512.11946 · HTML: https://mlsanity.com/paper/2512.11946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Explainable Machine Learning for Scientific Insights and Discoveries](https://mlsanity.com/paper/1905.08883/) (2019)
- [Principles and Practice of Explainable Machine Learning](https://mlsanity.com/paper/2009.11698/) (2020)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Decomposing Global Feature Effects Based on Feature Interactions](https://mlsanity.com/paper/2306.00541/) (2023)
- [Sensitivity analysis for multidimensional and functional outputs](https://mlsanity.com/paper/1311.1797/) (2013)
- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Exploration](https://mlsanity.com/paper/2503.19496/) (2025)
- [Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling](https://mlsanity.com/paper/2310.09194/) (2023)

## Abstract (arXiv)

Explainable machine learning techniques have gained increasing attention in engineering applications, especially in aerospace design and analysis, where understanding how input variables influence data-driven models is essential. Partial Dependence Plots (PDPs) are widely used for interpreting black-box models by showing the average effect of an input variable on the prediction. However, their global sensitivity metric can be misleading when strong interactions are present, as averaging tends to obscure interaction effects. To address this limitation, we propose a global sensitivity metric based on Individual Conditional Expectation (ICE) curves. The method computes the expected feature importance across ICE curves, along with their standard deviation, to more effectively capture the influence of interactions. We provide a mathematical proof demonstrating that the PDP-based sensitivity is a lower bound of the proposed ICE-based metric under truncated orthogonal polynomial expansion. In addition, we introduce an ICE-based correlation value to quantify how interactions modify the relationship between inputs and the output. Comparative evaluations were performed on three cases: a 5-variable analytical function, a 5-variable wind-turbine fatigue problem, and a 9-variable airfoil aerodynamics case, where ICE-based sensitivity was benchmarked against PDP, SHapley Additive exPlanations (SHAP), and Sobol' indices. The results show that ICE-based feature importance provides richer insights than the traditional PDP-based approach, while visual interpretations from PDP, ICE, and SHAP complement one another by offering multiple perspectives.